¶1 In this appeal, we are asked to address whether the juvenile court properly terminated E.M.'s (Father) parental rights to N.M. (Child). For the reasons explained below, we affirm.
BACKGROUND
Child's Removal and the Initial Permanency Proceedings
¶2 In an April 2015 shelter proceeding, the juvenile court determined that Child's removal from Father and Child's mother (Mother) was necessary and in Child's best interest due to both parents' incarceration. The court thereafter adjudicated Child neglected as to both Father and Mother, and it placed Child in the custody of the Division of Child and Family Services (DCFS). DCFS created a family plan for both Father and Mother and recommended reunification as the primary permanency goal, with Child's adoption as the concurrent goal. The court accepted the proposed plan as well as the stated goals and ordered DCFS to make "reasonable effort to finalize the permanency goal." In November 2015, given Father's and Mother's respective lack of progress, the court granted temporary custody and guardianship of Child to his maternal grandparents (Maternal Grandparents), subject to DCFS supervision. Child remained with Maternal Grandparents from then on.
¶3 The court thereafter terminated reunification services for both parents and, accordingly, in a September 2016 permanency hearing, changed the permanency goal to adoption, with the concurrent goal of permanent custody and guardianship with Maternal Grandparents. The court also determined that Child's best interest required a petition for termination of parental rights to be filed, and it ordered that such a petition be filed, and a pretrial hearing held, within forty-five days.1
¶4 Following the permanency order, the State filed a petition for termination of parental rights (the TPR) as to both parents. In it, the State recited the case history, which included the fact that both parents had "serious" substance abuse problems and that neither parent had remedied the circumstances that led to Child's out-of-home placement. The State asserted that it would be in Child's best interest for Father's and Mother's parental rights to be terminated, that Child was in need of permanency, and that Child needed to be available for adoption to achieve that permanence. The court ordered the parents to participate in mediation and set the TPR for a pretrial hearing on November 16, 2016.
*1242The November 2016 Pretrial Hearing
¶5 At the pretrial hearing, rather than proceeding with the TPR, the State moved to change the temporary custody in Maternal Grandparents to permanent custody and guardianship and to dismiss the TPR. The State declared that "there are some burdens of proof ... that would be very difficult to be able to carry forward" and that its request "would be in the child's best interest."
¶6 In response, the court noted that adoption was the permanency goal in the case, and it heard from those present regarding the State's request to grant permanent custody and guardianship to Maternal Grandparents. The State, the Guardian ad Litem, and the parents agreed that permanent custody and guardianship would be in Child's best interest. Maternal Grandparents stated that their desire was to adopt Child.
¶7 After hearing from those present, the court expressed concern that granting the State's request to "set the goal at permanent custody and guardianship" would only delay the proceedings and increase the uncertainty in Child's life. The court then stated:
[I]n this particular case I'm not ready to name permanent custody and guardianship as the permanency goal. We have a young child here of tender age and young age, and I appreciate everything that's been said in this matter, but it's the Court's decision what the permanency goal should be. It very well may end up being permanent custody and guardianship, but I don't have the evidence before me and I feel like I need to hear that evidence.
¶8 Mother objected, stating that the court did have evidence and knew "almost everything" about the case. The State also objected, asserting that it did not think it could "carry the burden of proof" if it went to trial on the TPR. In response, the court stated,
[T]he Court set the permanency goal of adoption, and we'll hear the evidence that's involved. Whether you think the burden is there or not, that's the job for the Court to decide; and very well it may not be, and I'll make a decision for permanent custody and guardianship, but there isn't a stipulation in this matter. The grandparents have voiced their concerns and I want to hear the evidence.
¶9 The court therefore denied the State's request to dismiss the TPR and order permanent custody and guardianship in Maternal Grandparents, and it set the case for a termination trial in January 2017.
The Pretrial Motions
¶10 Before the termination trial began, both the State and the parents filed additional documents with the court. First, the State filed a notice to withdraw the TPR. Next, Father and Mother filed a joint rule 60(b) motion, asking the court to set aside its November 16 order denying the State's oral request to dismiss the TPR. Father and Mother argued that the court should set aside its order because the State conceded that it could not meet its burden of proof at trial. The parents contended that the State, not the court, decides which cases to file, litigate, and prosecute. The parents also argued that requiring the State to proceed with the termination trial effectively forced it to violate rule 3.1 of the Utah Rules of Professional Conduct, which provides that a lawyer "shall not bring or defend a proceeding, or assert or controvert an issue therein, unless there is a basis in law and fact for doing so."
¶11 In the alternative, the parents argued that the court should treat the State's November 16 oral motion to dismiss the TPR as a rule 41 notice of dismissal under the Utah Rules of Civil Procedure. The parents claimed that, because the parties stipulated to the dismissal of the TPR, the court lost jurisdiction over the petition while still retaining jurisdiction to enter an order of permanent custody and guardianship in line with the court's concurrent goal. The parents also noted that Maternal Grandparents would be free to file their own termination petition.
¶12 On January 17, 2017, the court denied the parents' rule 60(b) motion and struck the State's notice of withdrawal.
The Termination Trial
¶13 The case proceeded to the termination trial. On the second day of trial, Mother advised the court that she wished to relinquish her parental rights to Child to allow Maternal Grandparents to adopt Child. The court took Mother's voluntary relinquishment *1243under advisement. The State thereafter clarified that, given Mother's voluntary relinquishment, it had "no misgivings about going forward with and putting on whatever evidence was necessary to establish [Father's] unfitness." The State explained that, although it had asserted in the November 2016 hearing that it did not have enough evidence to proceed with a termination trial, its reservation applied only to the evidence with respect to Mother, not to Father. The State asserted that it had "never questioned the evidence with respect to [Father]," that Father had "never done anything" to establish his fitness as a parent, and that he accordingly was unfit. The State ultimately contended that it was in Child's best interest for the court to grant the TPR with respect to Father.
¶14 In February 2017, the court entered a termination order, terminating both Mother's and Father's parental rights as to Child. The court accepted Mother's voluntary relinquishment of her parental rights. As to Father, the court determined that he was an unfit parent and that it would be in Child's best interest to terminate Father's parental rights. In doing so, the court noted that, while having Child "in a permanent custody and guardianship arrangement may be convenient for Father, ... it is not in [Child's] best interest." The court observed that Child instead needed "the certainty and benefits that come with being adopted." Accordingly, the court determined that it was "strictly and absolutely necessary to terminate parental rights so Maternal Grandparents can adopt [Child]," and it ordered Child to remain in Maternal Grandparents' custody until he was adopted.
¶15 Father appeals the juvenile court's denial of his rule 60(b) motion and the court's termination of his parental rights as to Child.
ANALYSIS
I. Failure to Accept the Parties' Stipulation about the Permanency Goal
¶16 Father first argues that the juvenile court erred "in applying the law by failing to accept [the parties'] stipulation" that it would be in Child's best interest to change the permanency goal from adoption to permanent custody and guardianship with Maternal Grandparents. In particular, Father claims that the juvenile court was "bound by the parties' stipulation" and that the court erred in disregarding it.
¶17 Father's request that the juvenile court honor the parties' stipulation appeared in his joint rule 60(b) motion for relief from the court's November 2016 oral ruling, which the court denied and later incorporated into the termination order. We generally review both a court's denial of a rule 60(b) motion and a refusal to accept an alleged stipulation for an abuse of discretion. See generally Fisher v. Bybee , 2004 UT 92, ¶ 7, 104 P.3d 1198 (reviewing a denial of a rule 60(b) motion); Jensen v. Jensen , 2008 UT App 392, ¶ 6, 197 P.3d 117 (reviewing a district court's refusal to accept a stipulation). And here, we conclude that the court did not exceed its discretion when it declined to adopt the proffered stipulation. Father's overall argument-that the juvenile court was bound by the parties' stipulation-is at odds both with precedent establishing a juvenile court's inherent discretion to disregard stipulations that intrude upon its core responsibilities and with the overarching purpose of juvenile courts in protecting a child's best interest throughout child welfare and permanency proceedings.
¶18 The Utah Supreme Court has explained that, while "the law favors the settlement of disputes" through agreements between parties, there are circumstances in which it is appropriate for a court to disregard such agreements and stipulations. See In re E.H. , 2006 UT 36, ¶¶ 20-21, 137 P.3d 809. Put plainly, a court may disregard stipulations that "compromise the core responsibilities of the court." See id. ¶ 21. For example, a court may, pursuant to its fact-finding responsibility, disregard agreements regarding certain facts and instead "compel the parties to present evidence for the court to weigh and evaluate." Id. ¶ 20 ; In re D.A.J. , 2015 UT App 74, ¶ 6, 347 P.3d 430 (per curiam) (same). A court also must "exercise greater care when delegating judicial functions" in cases "where considerations of public policy or fundamental constitutional rights permeate a case." See *1244In re E.H. , 2006 UT 36, ¶ 26, 137 P.3d 809. Child welfare and adoption cases are such cases. See id. ; see also Utah Code Ann. § 78A-6-102(5) (LexisNexis 2012) (outlining the purposes of the juvenile courts); In re M.H. , 2014 UT 26, ¶ 44, 347 P.3d 368 (Nehring, J., concurring in the result) (explaining that when the Juvenile Court Act was enacted its purpose was to "act in the interest of Children in various kinds of troubled circumstances because of the public interest in their welfare" (quotation simplified) ).
¶19 To that end, juvenile courts have exclusive jurisdiction over proceedings involving abused, neglected, or dependent children within the statutory definitions, including termination proceedings. Utah Code Ann. § 78A-6-103(1)(b), (f) (LexisNexis Supp. 2017); see also In re D.A.J. , 2015 UT App 74, ¶ 5, 347 P.3d 430. And one of the juvenile court's main purposes and responsibilities in these types of proceedings is to "act in the best interests of the minor in all cases." Utah Code Ann. § 78A-6-102(5)(g) (2012). Indeed, the Juvenile Court Act provides that the court overseeing permanency proceedings "shall ... consider the welfare and best interest of the child of paramount importance" in rendering its permanency determinations. See id. § 78A-6-503(12) (LexisNexis Supp. 2017); see also id. § 78A-6-506(3) (2012); In re M.H. , 2014 UT 26, ¶ 44, 347 P.3d 368 (explaining that the "best interests of the children remains the guiding principle in juvenile court proceedings today" and that "the purpose of the juvenile courts [is] to strive to act in the best interests of the children in all cases" (quotations simplified) ); In re J.D. , 2011 UT App 184, ¶¶ 10, 24, 26, 257 P.3d 1062 (affirming that "in every [termination of parental rights] case, the best interest of the child is of paramount importance in determining whether the child-parent relationship should be permanently severed").
¶20 In this regard, our supreme court has explained that the court overseeing these types of proceedings retains the "final authority over the determination of [a child's] best interests." See In re E.H. , 2006 UT 36, ¶¶ 28, 37, 137 P.3d 809. This core authority to determine a child's best interest cannot be stipulated away by the parties. See id. ¶¶ 21-28, 37 ; see also R.B. v. L.B. , 2014 UT App 270, ¶¶ 14-17, 339 P.3d 137 ("[P]arties cannot stipulate away the district court's statutory responsibility to conduct a best-interest analysis."); see generally Utah Code Ann. §§ 78A-6-503(12), -506(3) (LexisNexis 2012 & Supp. 2017) (providing that the court determines whether termination is appropriate in light of "the welfare and best interest of the child," which is "of paramount importance" (emphasis added) ).
¶21 For example, in In re adoption of J.M ., 2005 UT App 157, 135 P.3d 902 (per curiam), although the father delegated his parental powers through a signed statement to his own parents, the juvenile court instead awarded temporary guardianship to the maternal grandparents. Id. ¶¶ 1-2. On appeal, the paternal grandparents argued that "the delegation of parental powers trumps the juvenile court's power to determine guardianship of the child." Id. ¶ 2. This court disagreed, noting that "[n]o provision in the Utah Code regulating the juvenile court limits the juvenile court's authority when a delegation of parental power has been signed." Id. ¶¶ 2-3. And we observed that "[t]o hold otherwise would allow any parent in danger of having their parental rights terminated a means of divesting the juvenile court of its power to protect the best interests of children"-an untenable proposition, given the juvenile court's ultimate authority to determine what is or is not in a child's best interest. See id.
¶22 Similarly, in In re D.A.J. , a private party filed a petition to terminate the mother's parental rights and, in the course of the proceedings, the mother and the private party entered into a stipulation "that addressed many issues related to the custody and care" of the child. 2015 UT App 74, ¶ 2, 347 P.3d 430. When the juvenile court dismissed the termination petition after determining that grounds for termination were not established and termination was not in the child's best interest, the private party appealed, arguing that the stipulation "established that [the child] was dependent" and, notwithstanding the dismissal of the termination petition, the juvenile court should grant the private party custody and guardianship of the child. Id. ¶¶ 3-4. We rejected those arguments, concluding that the juvenile court was not bound by the stipulation at issue. Id. ¶¶ 6-7. We *1245determined that, regardless of the stipulation, the juvenile court had not adjudicated the child as dependent and that parties cannot stipulate to a juvenile court's subject matter jurisdiction, such as through an agreement about a child's alleged dependency. Id. ¶ 6. We also reiterated that the court retained discretion to disregard "an agreement regarding certain facts" and could instead compel the parties to present evidence on the issue. Id.
¶23 Here, the stipulation upon which Father relies represented the parties' determination that, rather than terminate Father's parental rights and proceed with the primary permanency goal of adoption, it would be in Child's best interest to place Child in the permanent custody and guardianship of Maternal Grandparents. Nevertheless, because that stipulation was necessarily predicated upon a determination by the parties regarding what was in Child's best interest, the court was not bound by it or obligated to accept it. See In re E.H. , 2006 UT 36, ¶¶ 21-28, 37, 137 P.3d 809. As we have explained above, one of the juvenile court's core responsibilities is protecting and making determinations regarding a child's best interest. Thus, the juvenile court, not the parties, retains the final authority to determine, once reunification services to both parents are terminated, what permanency goal-permanent custody and guardianship or adoption-would be in a child's best interest. See id. ; see generally Utah Code Ann. § 78A-6-314 (LexisNexis Supp. 2017) (authorizing a court to determine a final plan in the child's best interest in circumstances where, among other things, reunification services were not successful). The court here acted well within its discretion and its authority, as overseer of the permanency proceedings and final arbiter of Child's best interest, to reject the parties' proffered stipulation and instead continue with the termination proceedings to hear the available evidence before making its final permanency determinations.2 Accordingly, we conclude that the juvenile court did not err in terminating Father's parental rights.3
II. Failure to Dismiss the TPR
¶24 Father also argues that the juvenile court erred by declining to treat the State's motion to change the permanency goal and dismiss the TPR as a voluntary dismissal under rule 41 of the Utah Rules of Civil Procedure, a dismissal he claims ought to have resulted in the juvenile court's loss of jurisdiction over the TPR. In particular, he claims that the court erred because the State's "oral request was proper" under rule 41.
¶25 Father asked the juvenile court in his joint rule 60(b) motion to treat the State's oral motion to change the permanency goal and dismiss the TPR as a rule 41 voluntary dismissal. We generally review for an abuse of discretion the court's refusal to grant relief on this basis.
*1246Fisher v. Bybee , 2004 UT 92, ¶ 7, 104 P.3d 1198 ("We will generally reverse a [lower] court's denial of a rule 60(b) motion only where the court has exceeded its discretion."). However, even if the juvenile court exceeded its discretion in failing to grant the relief Father requested, Father is entitled to relief on appeal only if he can also demonstrate that he was harmed by the alleged error. See In re P.D. , 2013 UT App 162, ¶ 11, 306 P.3d 817 ("On appeal, the appellant has the burden of demonstrating an error was prejudicial-that there is a reasonable likelihood that the error affected the outcome of the proceedings." (quotation simplified) ). We conclude that Father's rule 41 challenge fails because, as we explain below, he has not shown that he was harmed by the alleged error.
¶26 Rule 41 provides in relevant part that a plaintiff may voluntarily "dismiss an action without a court order by filing ... a notice of dismissal before the opposing party serves an answer or a motion for summary judgment; or ... a stipulation of dismissal signed by all parties who have appeared." Utah R. Civ. P. 41(a)(1)(A). A valid voluntary dismissal under this rule renders the proceedings a "nullity," because "no case in controversy exists any longer and, hence, the court ... lack[s] jurisdiction to proceed any further with the action." Thiele v. Anderson , 1999 UT App 56, ¶ 24, 975 P.2d 481 (quotations simplified). Father claims that the court erred in failing to dismiss the TPR because the State's request, memorialized by its later notice of withdrawal, constituted a rule 41 notice of dismissal made before the parents had answered the TPR.
¶27 Even assuming for purposes of argument that the court ought to have construed the State's request as a rule 41 dismissal and that it was error not to do so, Father has not demonstrated that the juvenile court's alleged error was harmful. See In re J.B. , 2002 UT App 268, ¶¶ 8-12, 53 P.3d 968 (affirming the termination of a father's parental rights where, even though the juvenile court erred in relying upon findings from a prior termination proceeding in which the father did not participate to terminate the mother's rights, the error was not harmful). "The pivotal question is whether the error resulted in prejudice sufficient to warrant reversal of the termination order. An error is prejudicial only if a review of the record persuades the appellate court that without the error there was a reasonable likelihood of a more favorable result for the [appellant]." In re C.Y. , 765 P.2d 251, 254 (Utah Ct. App. 1988) (quotation simplified); see also Albrecht v. Bennett , 2002 UT App 64, ¶¶ 31-32, 44 P.3d 838 (declining to reach the merits of an allegedly improper rule 41 dismissal where the alleged error was harmless in light of the record and the other proceedings in the case). Father contends, in conclusory fashion, that had the TPR been dismissed, the State would not have been forced "to pursue termination against him," and the court would have instead "properly mov[ed] towards its concurrent goal of permanent custody and guardianship as stipulated to by the parties."
¶28 But Father has not shown that, if the TPR had been dismissed, the court would have "mov[ed] towards its concurrent goal of permanent custody and guardianship." As we have explained, the court was not required to simply accept on motion that permanent custody and guardianship would have been in Child's best interest, and Father has not shown that, had the TPR been dismissed, the court necessarily would have abandoned its primary permanency goal of adoption. To the contrary, in the November 2016 hearing, the juvenile court expressed its discomfort with proceeding with the concurrent goal precisely because it did not believe it had the evidence yet that it was in Child's best interest to do so. See generally In re M.H. , 2014 UT 26, ¶ 44, 347 P.3d 368 (Nehring, J., concurring in the result) (explaining that the "best interests of the children remains the guiding principle in juvenile court proceedings today" and that "the purpose of the juvenile courts [is] to strive to act in the best interests of the children in all cases" (quotations simplified) ). Nor has Father provided any authority to support the proposition that in circumstances in which a termination petition is dismissed a juvenile court is required to abandon the primary permanency goal and instead proceed under the concurrent goal. See Bank of Am. v. Adamson , 2017 UT 2, ¶¶ 11-13, 391 P.3d 196 (suggesting that an appellant will not carry his burden of persuasion on appeal if the appellant fails to "cite the legal authority *1247on which [his] argument is based and then provide reasoned analysis of how that authority should apply in the particular case"); see generally Utah Code Ann. § 78A-6-312(10)(a)-(b) (LexisNexis Supp. 2017) (providing that the juvenile court "may amend a minor's primary permanency plan before the establishment of a final permanency plan," but that "[t]he court is not limited to the terms of the concurrent permanency plan in the event that the primary permanency plan is abandoned").
¶29 In this regard, Father has provided little basis for his prediction about how the case would have proceeded. Even had the TPR been dismissed, the court retained jurisdiction over Child by virtue of Child's adjudication as neglected, see generally Utah Code Ann. § 78A-6-103(1)(b) (Supp. 2017) (providing that the juvenile court has exclusive jurisdiction over a neglected child), and its September 2016 decisions-terminating reunification services, setting adoption as the final permanency goal, and ordering that a petition for termination of both parents' rights be filed-still stood. Father has not shown, for example, that in these circumstances it was reasonably likely that another interested party-such as Maternal Grandparents or the Guardian ad Litem-would have failed to file a termination petition pursuant to the court's permanency order, had the State's petition been dismissed. See generally id. § 78A-6-504(1) (2012) (providing that "[a]ny interested party, including a foster parent, may file a petition for termination of the parent-child relationship with regard to a child"). And, regardless of whether the TPR was dismissed under rule 41, given the termination of reunification services, the court still would have had to decide whether adoption or permanent custody and guardianship was the proper permanent plan for Child. See id. § 78A-6-314(4) (Supp. 2017). To make that decision, the court would have had to consider the evidence relevant to that question, just as it had pursuant to its decision to terminate Father's parental rights. Father therefore has not demonstrated that, given the posture of the case, even if the TPR had been dismissed, the case was reasonably likely to have proceeded differently, resulting in a different and more favorable outcome for him. See In re J.B. , 2002 UT App 268, ¶¶ 8-12, 53 P.3d 968.
¶30 Accordingly, Father has not shown he is entitled to relief on appeal. On this basis, we reject his rule 41 challenge to the termination of his parental rights.
CONCLUSION
¶31 We reject Father's argument that the juvenile court erred by failing to accept the parties' stipulation regarding Child's best interest. We also reject Father's challenge to the juvenile court's refusal to dismiss the TPR on the basis of rule 41 of the Utah Rules of Civil Procedure. Accordingly, we affirm the termination of Father's parental rights as to Child.