You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]



10 A.3d 115 (2011)
126 Conn.App. 185
WILLIAM C.[1]
v.
COMMISSIONER OF CORRECTION.
No. 31609.
Appellate Court of Connecticut.
Submitted on Briefs October 15, 2010.
Decided January 18, 2011.
Robert E. Byron, special public defender, filed a brief for the appellant (petitioner).
John A. Connelly, state's attorney, and Rita M. Shair and Angela R. Macchiarulo, *116 senior assistant state's attorneys, filed a brief for the appellee (respondent).
BISHOP, LAVINE and ALVORD, Js.
ALVORD, J.
The petitioner, William C., appeals following the habeas court's denial of his petition for certification to appeal from the judgment denying his amended petition for a writ of habeas corpus. On appeal, the petitioner claims that the court abused its discretion when it denied his petition for certification to appeal and improperly rejected his claim that his trial counsel had provided ineffective assistance. More specifically, the petitioner claims that there was merit to his claim of ineffective assistance of trial counsel because counsel failed to request a contemporaneous limiting instruction regarding the constancy of accusation testimony of six witnesses. We dismiss the appeal.
In 2005, following a jury trial, the petitioner was convicted of sexual assault in a spousal relationship in violation of General Statutes § 53a-70b (b).[2] At trial, J, the petitioner's wife at the time of the incident, testified that the petitioner sexually assaulted her in the early morning hours of October 3, 2002. After J's testimony, several witnesses testified that J had told them that the petitioner had sexually assaulted her on October 3, 2002. The petitioner did not request a limiting instruction with respect to the constancy of accusation testimony at the time it was given. The court did, however, address the limited purposes for which such testimony could be considered in its final charge to the jury. This court affirmed the judgments of conviction on direct appeal. See State v. William C., 103 Conn. App. 508, 930 A.2d 753, cert. denied, 284 Conn. 928, 934 A.2d 244 (2007).
The petitioner subsequently filed a petition for a writ of habeas corpus, in which he claimed that Michael Gannon, his trial counsel, had rendered ineffective assistance by failing to request that the jury be given a limiting instruction at the time of the testimony of each of the constancy of accusation witnesses.[3] In discussing the petitioner's claim, the habeas court first noted that the petitioner had been represented by Gannon and attorney Fanol Bojka at his criminal trial. Of the six constancy of accusation witnesses, Gannon cross-examined three of the witnesses, and Bojka cross-examined the remaining three. Neither attorney had requested a limiting instruction immediately prior to or following the constancy of accusation testimony. The ineffective assistance of counsel claim, however, is directed only to Gannon's representation.
The habeas court then concluded that the petitioner had not demonstrated that he had been prejudiced by Gannon's failure to request the limiting instructions even if the court had assumed that his performance had been deficient. The court reached this conclusion because the *117 trial court had instructed the jury in its final charge as to the proper use of the constancy of accusation testimony. The habeas court indicated that there had been no showing that the jury failed to follow the court's instructions, and, therefore, the petitioner failed to prove ineffective assistance of counsel. Accordingly, the court denied the habeas petition and denied the petition for certification to appeal from the judgment. This appeal followed.
"We begin by setting forth the applicable standard of review. Faced with a habeas court's denial of a petition for certification to appeal, a petitioner can obtain appellate review of the dismissal of his petition for habeas corpus only by satisfying the two-pronged test enunciated by our Supreme Court in Simms v. Warden, 229 Conn. 178, 640 A.2d 601 (1994), and adopted in Simms v. Warden, 230 Conn. 608, 612, 646 A.2d 126 (1994). First, he must demonstrate that the denial of his petition for certification constituted an abuse of discretion. ... Second, if the petitioner can show an abuse of discretion, he must then prove that the decision of the habeas court should be reversed on its merits. ...
"To prove an abuse of discretion, the petitioner must demonstrate that the [resolution of the underlying claim involves issues that] are debatable among jurists of reason; that a court could resolve the issues [in a different manner]; or that the questions are adequate to deserve encouragement to proceed further. ...
"We examine the petitioner's underlying claim of ineffective assistance of counsel in order to determine whether the habeas court abused its discretion in denying the petition for certification to appeal. Our standard of review of a habeas court's judgment on ineffective assistance of counsel claims is well settled. In a habeas appeal, this court cannot disturb the underlying facts found by the habeas court unless they are clearly erroneous, but our review of whether the facts as found by the habeas court constituted a violation of the petitioner's constitutional right to effective assistance of counsel is plenary." (Internal quotation marks omitted.) Earl G. v. Commissioner of Correction, 106 Conn.App. 758, 760-61, 943 A.2d 1118, cert. denied, 288 Conn. 901, 952 A.2d 809 (2008).
"In Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the United States Supreme Court enunciated the two requirements that must be met before a petitioner is entitled to reversal of a conviction due to ineffective assistance of counsel. First, the [petitioner] must show that counsel's performance was deficient. ... Second, the [petitioner] must show that the deficient performance prejudiced the defense. ... Unless a [petitioner] makes both showings, it cannot be said that the conviction ... resulted from a breakdown in the adversarial process that renders the result unreliable." (Internal quotation marks omitted.) McClam v. Commissioner of Correction, 98 Conn.App. 432, 436, 909 A.2d 72 (2006), cert. denied, 281 Conn. 907, 916 A.2d 49 (2007). "A reviewing court need not address both components of the inquiry if the [petitioner] makes an insufficient showing on one." (Internal quotation marks omitted.) Smith v. Commissioner of Correction, 89 Conn.App. 134, 139, 871 A.2d 1103, cert. denied, 275 Conn. 909, 882 A.2d 676 (2005).
With this standard in mind, we conclude that the habeas court correctly determined that the petitioner failed to demonstrate that his defense was prejudiced by Gannon's failure to request a limiting instruction immediately before or after the constancy of accusation testimony of the three witnesses that he cross-examined. *118 Although the petitioner argues that an instruction at the end of trial does not redeem the error of failing to give a limiting instruction contemporaneously with the constancy of accusation testimony, he cites no Connecticut case law that supports his argument. In fact, our case law in this regard is to the contrary.
"[A]lthough it is acceptable for a trial court, in its discretion, to give a contemporaneous limiting instruction to the jury, there is no rule of practice or statutory requirement that the court must give such an instruction contemporaneously with the introduction of such testimony." Lemoine v. Commissioner of Correction, 73 Conn.App. 669, 676, 808 A.2d 1194 (2002), cert. denied, 262 Conn. 932, 815 A.2d 133 (2003). It is undisputed that the trial court did instruct the jury as to the proper use of constancy of accusation testimony in its final charge. Significantly, the petitioner has not claimed that the court's instruction on the use of constancy of accusation testimony was inadequate or contrary to law.[4] It is well established that "[t]he jury is presumed, in the absence of a fair indication to the contrary, to have followed the court's instructions." (Internal quotation marks omitted.) State v. Wallace, 290 Conn. 261, 276, 962 A.2d 781 (2009); State v. McKenzie-Adams, 281 Conn. 486, 544, 915 A.2d 822, cert. denied, 552 U.S. 888, 128 S.Ct. 248, 169 L.Ed.2d 148 (2007).
Thus, in the context of this ineffective assistance of counsel claim, the absence of a limiting instruction at the time that the constancy of accusation testimony was presented did not prejudice the petitioner. In light of the foregoing conclusions, the petitioner has not demonstrated that the issues raised with regard to the court's denial of his petition for a writ of habeas corpus are debatable among jurists of reason, that a court could resolve the issues in a different manner or that the questions raised deserved encouragement to proceed further. See Simms v. Warden, supra, 230 Conn. at 616, 646 A.2d 126. Accordingly, we conclude that the court did not abuse its discretion in denying the petition for certification to appeal.
The appeal is dismissed.
In this opinion the other judges concurred.
NOTES
[1]  In accordance with our policy of protecting the privacy interests of the victims of sexual abuse, we decline to identify the victim or others through whom the victim's identity may be ascertained. See General Statutes § 54-86e.
[2]  The petitioner was also convicted of unlawful restraint in the first degree in violation of General Statutes § 53a-95 (a), breach of the peace in the second degree in violation of General Statutes § 53a-181, threatening in the second degree in violation of General Statutes § 53a-62 (a)(1) and larceny in the sixth degree in violation of General Statutes § 53a-125b (a). State v. William C., 103 Conn.App. 508, 510, 930 A.2d 753, cert. denied, 284 Conn. 928, 934 A.2d 244 (2007). The petitioner's issue on appeal pertains to his conviction of the charge of sexual assault in a spousal relationship.
[3]  The petitioner's amended petition for a writ of habeas corpus included several other claims of ineffective assistance of trial counsel. The petitioner has not appealed from the habeas court's rulings on those additional claims.
[4]  The court's charge on constancy of accusation testimony included the following: "The complainant testified here in court before you. Her testimony in court you may use as evidence and proof of the facts asserted in that testimony and give it the weight you find is reasonable.

"The state offered evidence of out-of-court statements made by the complainant to other persons that the [petitioner] sexually assaulted her. These persons to whom she may have made such statements are [N], [H], [M], [K], [A] and [J]. Each of these people testified as to the statements the complainant made to each of them regarding the [petitioner] sexually assaulting her.
"This constancy of accusation evidence by each of these witnesses is admitted solely, remember this, solely to corroborate or not corroborate her testimony here in court.
"The constancy of accusation testimony was allowed for the sole purpose of showing that the complainant made the statements to these individuals. These out-of-court constancy of accusation statements are not substantive evidence and are to be considered by you only in determining the weight and credibility you will accord the complainant's testimony given here in court. The evidence of the out-of-court statements by her of a sexual assault against her by the [petitioner] is not to be considered by you to prove the truth of the matter asserted in those out-of-court statements."
The court provided a copy of its written instructions to the jury as a court exhibit.