*190The petitioner, Eric White, appeals from the judgment of the habeas court denying his amended petition for a writ of habeas corpus. On appeal, the petitioner claims that the court improperly rejected his claims that (1) his right to due process was violated because his guilty plea was not made knowingly, intelligently and voluntarily *174and (2) his right to effective assistance of counsel was violated because his attorney failed to adequately research and investigate the issue of the petitioner's mental state at the time of his guilty plea and to bring information about the petitioner's compromised mental state to the attention of the criminal trial court. We disagree and, accordingly, affirm the judgment of the habeas court.
The following facts and procedural history are relevant to this appeal. On August 11, 2004, the petitioner, represented by Attorney Joseph Bruckmann, pleaded guilty under the Alford1 doctrine to one count of felony murder in violation of General Statutes §§ 53a-54c and 53a-54a(a). The trial court indicated that it intended to *191sentence the petitioner to fifty years of imprisonment, which it did on November 5, 2004. The petitioner did not appeal from his conviction following his plea and sentencing or file any postjudgment motions.
The petitioner petitioned for a writ of habeas corpus on January 8, 2014. After counsel was appointed, the petitioner filed an amended petition on May 23, 2016, asserting that Bruckmann had provided ineffective assistance of counsel and that the petitioner's due process rights had been violated because his guilty plea was not made knowingly, intelligently and voluntarily. The thrust of his claims was that medication the petitioner was taking on the day of his guilty plea "substantially impacted his ability to understand the plea agreement and the plea proceedings," that he would not have entered a guilty plea had he not been so medicated, and that Bruckmann was ineffective for failing to research and investigate the issue regarding his mental condition or to bring such information to the court's attention. (Internal quotation marks omitted.)
At the habeas trial on September 19, 2016, Bruckmann, the petitioner, and the petitioner's psychiatric expert, James Phillips, testified. The petitioner also entered into evidence the transcripts of his guilty plea and sentencing, and medical records detailing his medication usage around the time of his guilty plea. The respondent, the Commissioner of Correction, offered no evidence.
On September 27, 2016, the habeas court issued its memorandum of decision denying the amended petition for a writ of habeas corpus. The court credited the testimony of Bruckmann and Phillips in determining that the petitioner had failed to establish ineffective assistance of counsel or a due process violation.2 In *192evaluating the transcripts in evidence, the court observed that Bruckmann and the trial court made the petitioner aware "of all necessary information to make an informed decision ... whether to enter a plea or take his case to trial." In considering the petitioner's own testimony, although the habeas court did not find that testimony completely lacking in credibility, it found that such testimony was "wholly insufficient to prove any of the necessary elements to establish either a due process violation or a claim of ineffective assistance of counsel. Contrasted with the other, more credible evidence adduced at trial, the petitioner's proffered evidence in support of his claims borders on the frivolous." *175The petitioner petitioned the habeas court for certification to appeal, which the court granted. This appeal followed.
We begin with generally applicable legal principles. "The underlying historical facts found by the habeas court may not be disturbed unless the findings were clearly erroneous.... Historical facts constitute a recital of external events and the credibility of their narrators.... Questions of law and mixed questions of law and fact receive plenary review." (Internal quotation marks omitted.) Crawford v. Commissioner of Correction , 294 Conn. 165, 174, 982 A.2d 620 (2009). "The application of the habeas court's factual findings to the pertinent legal standard ... presents a mixed question of law and fact ...." Duperry v. Solnit , 261 Conn. 309, 335, 803 A.2d 287 (2002).
I
The petitioner first claims that the habeas court erred in failing to find that his due process rights were violated *193because his underlying guilty plea was not made knowingly, intelligently and voluntarily. Specifically, he argues that the medication he was taking at the time of his guilty plea "completely undermined his ability to meaningfully consider his decision to plead guilty [and] interfered with his ability to understand the plea agreement and the guilty plea proceeding." We disagree.
"[T]he guilty plea and subsequent conviction of an accused person who is not legally competent to stand trial violates the due process of law guaranteed by the state and federal constitutions.... This constitutional safeguard, which is codified at General Statutes § 54-56d(a), provides that [a] defendant shall not be tried, convicted or sentenced while the defendant is not competent.... [A] defendant is not competent if the defendant is unable to understand the proceedings against him or her or to assist in his or her own defense....
"[T]he test for competency must be whether [the defendant] has sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding-and whether he has a rational as well as factual understanding of the proceedings against him....
"Although § 54-56d(b) presumes the competency of defendants, when a reasonable doubt concerning the defendant's competency is raised, the trial court must order a competency examination.... Thus, [a]s a matter of due process, the trial court is required to conduct an independent inquiry into the defendant's competence whenever he makes specific factual allegations that, if true, would constitute substantial evidence of mental impairment.... Evidence is substantial if it raises a reasonable doubt about the defendant's competency ....
*194"[D]ue process requires that a plea be entered voluntarily and intelligently.... Because every valid guilty plea must be demonstrably voluntary, knowing and intelligent, we require the record to disclose an act that represents a knowing choice among available alternative courses of action, an understanding of the law in relation to the facts, and sufficient awareness of the relevant circumstances and likely consequences of the plea.... A determination as to whether a plea has been knowingly and voluntarily entered entails an examination of all of the relevant circumstances.... A defendant who suffers from a mental or emotional impairment is not necessarily incompetent to enter a guilty plea because [c]ompetence ... is not defined in terms of mental illness. An accused may be suffering from a mental *176illness and nonetheless be able to understand the charges against him and to assist in his own defense .... Similarly, [t]he fact that the defendant was receiving medication ... [of itself] does not render him incompetent.... The touchstone of competency, rather, is the ability of the defendant to understand the proceedings against him and to assist in his own defense." (Citations omitted; footnotes omitted; internal quotation marks omitted.) Taylor v. Commissioner of Correction , 284 Conn. 433, 449-52, 936 A.2d 611 (2007).
The habeas court found no due process violation. In its memorandum of decision, the habeas court first found that the petitioner's guilty plea canvass was constitutionally sufficient, noting that the petitioner had denied having taken any drugs, alcohol, or medication that day. The court also noted that the petitioner indicated at his plea proceeding that he and Bruckmann had discussed the case, including the underlying elements of the charges. The habeas court also observed that the trial court had indicated the sentence it intended to impose on a later date. The petitioner reaffirmed his *195understanding of the decision to plead guilty and accept a fifty year sentence.
The habeas court also considered the transcript of the petitioner's sentencing, where the petitioner accepted responsibility for his actions and acknowledged that "fifty years is not enough" for his offense. (Internal quotation marks omitted.) The petitioner gave no indication that he wanted to withdraw his plea. The petitioner did acknowledge taking medication at the time, but stated that it was for the purpose of falling asleep.
At the habeas trial, the petitioner testified that he was taking medication at the time of his guilty plea, although he could not recall what he was taking. He also testified that he continued taking medication until about six to eight months after he was sentenced, having taken himself off it because it "made [him] feel like [he] wasn't in the right state of mind half the time" and "a robot, a zombie ...." He claimed that these feelings affected his decision-making at and before the time he pleaded guilty because he did not always understand Bruckmann in their conversations before the plea.3
When the petitioner was asked why he denied taking any medication on the day of his plea, the petitioner claimed that he did not want to seem "insane" to the trial judge and that answering affirmatively would only have harmed him. Then, in response to a question regarding why he had pleaded guilty, the petitioner stated, "I [pleaded] guilty to benefit my family and to keep any more harm coming upon my family, so I just said, I understand and I [pleaded] guilty. I wanted to plead guilty to get it over with. Those were my exact words to [Attorney] Bruckmann. I want to get it over *196with to keep my mother from going through what she was going through." The petitioner then claimed that the medication he was taking affected these feelings. Finally, when asked why he was challenging his conviction almost ten years after his plea, he stated, "[w]ell, due to the fact that I've been incarcerated for fourteen years now and ... I had time to think about everything that happened ... and due to the fact that I'm older and I just feel like ... I have nothing to really lose from wanting my freedom back, and also my family." The petitioner then denied *177having waited ten years for evidence to be destroyed.
On cross-examination, the petitioner was asked again why he waited ten years to challenge his plea. He responded that he was scared and did not understand the law at the time. Counsel for the respondent then asked when the petitioner became aware that his medication was an issue. The petitioner responded that he became aware of that issue after sentencing. Finally, when asked why he had lied about not taking medication at his plea hearing, the petitioner said, "I thought it would help."
We conclude that the habeas court's findings are supported more than adequately by the record. The petitioner's responses to the trial court's questions during his canvass show that he fully understood the circumstances. "A court may properly rely on ... the responses of the [petitioner] at the time [he] responded to the trial court's plea canvass ...." (Internal quotation marks omitted.) Bigelow v. Commissioner of Correction , 175 Conn. App. 206, 215-16, 167 A.3d 1054, cert. denied, 327 Conn. 929, 171 A.3d 455 (2017). The petitioner's claim that he felt like a "zombie" and not in control of his actions is not borne out by the transcripts of the plea proceeding. Because the petitioner's expert offered no opinion as to the petitioner's mental state at the time of his plea; see footnote 3 of this *197opinion; the only evidence that could establish that the petitioner was not lucid at the time of his plea is his own testimony.4 Although the habeas court did not completely discredit the petitioner's testimony, it did not specifically credit anything to which he testified, stating instead that his evidence "border[ed] on the frivolous," and was insufficient to prove a due process violation.5 We are not at liberty to discard this credibility determination in deciding whether the petitioner's guilty plea was made knowingly, intelligently and voluntarily. The burden was on the petitioner to establish "a reasonable likelihood that the medication had adversely affected the petitioner's ability to understand the proceedings against him or to assist in his own defense." Taylor v. Commissioner of Correction , supra, 284 Conn. at 453, 936 A.2d 611. In the absence of any other convincing evidence to the contrary, we cannot say that the habeas court erred in not finding the relevant facts to establish a due process violation.
II
The petitioner also claims that the habeas court erred in not determining that his trial counsel provided ineffective assistance. Specifically, the petitioner argues that Bruckmann failed to research adequately and to investigate the issue of the petitioner's mental state at the time of his guilty plea, and to bring information about the petitioner's compromised mental state to the attention of the trial court. We are not persuaded.
*198"To prevail on a constitutional claim of ineffective assistance of counsel resulting from a guilty plea, a petitioner must establish both that his counsel's performance was deficient and that *178the deficient performance prejudiced him. See Hill v. Lockhart , 474 U.S. 52, 106 S.Ct. 366, 88 L.Ed. 2d 203 (1985) ; Strickland v. Washington , 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed. 2d 674 (1984) ; Baillargeon v. Commissioner of Correction , 67 Conn. App. 716, 721, 789 A.2d 1046 (2002). To satisfy the performance prong, the petitioner must show that counsel's representation fell below an objective standard of reasonableness.... To satisfy the prejudice prong, the petitioner must show a reasonable probability that, but for counsel's errors, he would not have pleaded guilty and would have insisted on going to trial.... A reviewing court can find against a petitioner on either ground, whichever is easier.... The petitioner cannot rely on mere conjecture or speculation to satisfy either the performance or prejudice prong but must instead offer demonstrable evidence in support of his claim." (Internal quotation marks omitted.) Cox v. Commissioner of Correction , 127 Conn. App. 309, 314, 14 A.3d 421, cert. denied, 301 Conn. 902, 17 A.3d 1043 (2011).
The habeas court, in its memorandum of decision, found that the petitioner failed to establish that Bruckmann rendered ineffective assistance. The court credited Bruckmann's testimony as to his numerous visits and discussions with the petitioner. Bruckmann had also testified that the petitioner wanted to enter the plea and accept his sentence and that it was clear to Bruckmann that the petitioner understood what he was doing, such that Bruckmann perceived no "red flags" concerning the petitioner's mental state. (Internal quotation marks omitted.) In addition, Bruckmann engaged the services of a forensic psychiatrist to evaluate the petitioner for any potential defenses to his murder *199charge. Bruckmann indicated that the psychiatrist reported no signs of psychosis or that the petitioner's mental health was an issue.
The petitioner argues that he was prejudiced because he would not have pleaded guilty but for Bruckmann's failure to adequately research and investigate the petitioner's mental state. He also argues that he was prejudiced because the trial court would not have accepted his guilty plea had Bruckmann not failed to bring to the attention of the trial court the petitioner's compromised mental state.6 His prejudice arguments necessarily depend on his argument that his mental state was compromised at the time of his pleas, which we determined was not borne out by the record in the context of his due process claim. See part I of this opinion. We likewise reject that argument underlying these claims of ineffective assistance. "Because the record before us does not evince that the petitioner was actually impaired by the use of any psychotropic drugs, we cannot conclude that his counsel was deficient in failing to investigate his mental ... health further." Hunnicutt v. Commissioner of Correction , 83 Conn. App. 199, 207, 848 A.2d 1229, cert. denied, 270 Conn. 914, 853 A.2d 527 (2004). Given Bruckmann's credited testimony that he perceived no "red flags," we likewise cannot conclude that Bruckmann was deficient for failing to bring the petitioner's mental state to the attention of the court, because such testimony is contraindicative of "a reasonable doubt concerning the [petitioner's] competency *179...." Taylor v. Commissioner of Correction , supra, 284 Conn. at 450, 936 A.2d 611. Even if we assume deficient performance, the record does not show "a *200reasonable probability that [the petitioner] would have chosen to proceed to trial rather than plead guilty" if Bruckmann had further investigated the petitioner's mental state or brought it to the trial court's attention. Hunnicutt v. Commissioner of Correction , supra, at 210, 848 A.2d 1229. Therefore, the habeas court did not err in concluding that Bruckmann did not render ineffective assistance of counsel.
The judgment is affirmed.
In this opinion the other judges concurred.