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]


ed without replacement from yayyyyyayyyyyyayyy.
5/34
Four letters picked without replacement from {d: 2, l: 7, i: 5}. Give prob of sequence ddli.
5/1716
Two letters picked without replacement from yhhyhy. What is prob of sequence hy?
3/10
Calculate prob of sequence trtr when four letters picked without replacement from rrrrrttr.
1/28
Four letters picked without replacement from wqqwwfz. What is prob of sequence qwwf?
1/70
Two letters picked without replacement from wsss. Give prob of sequence ss.
1/2
Three letters picked without replacement from vvevweovvesrvsr. What is prob of sequence svw?
2/455
Two letters picked without replacement from {f: 2, o: 2, y: 2, w: 3, b: 8}. What is prob of sequence fy?
1/68
What is prob of sequence ng when two letters picked without replacement from {b: 1, g: 6, n: 8, d: 1}?
1/5
Three letters picked without replacement from {x: 6, q: 2, d: 3, a: 2}. Give prob of sequence dqd.
1/143
Four letters picked without replacement from {b: 6, q: 3, c: 3, m: 3}. Give prob of sequence mbmb.
1/182
Three letters picked without replacement from {v: 4, u: 1, q: 6, x: 2, g: 4}. What is prob of sequence gqu?
1/170
Three letters picked without replacement from sxsxxxssxosswzs. Give prob of sequence ssx.
1/13
Calculate prob of sequence cy when two letters picked without replacement from {a: 1, c: 9, y: 1}.
9/110
Three letters picked without replacement from glggalgalggg. What is prob of sequence agl?
7/220
Two letters picked without replacement from lqqqqlqqlq. Give prob of sequence lq.
7/30
Three letters picked without replacement from {i: 5, n: 13}. What is prob of sequence iin?
65/1224
Four letters picked without replacement from {o: 4, k: 10}. What is prob of sequence ookk?
45/1001
Two letters picked without replacement from iiiiiiiii. What is prob of sequence ii?
1
Calculate prob of sequence aaa when three letters picked without replacement from {s: 2, a: 13, d: 5}.
143/570
Calculate prob of sequence sgh when three letters picked without replacement from {r: 2, k: 3, g: 1, h: 1, s: 7}.
1/312
What is prob of sequence gggg when four letters picked without replacement from {g: 10}?
1
Calculate prob of sequence wlgh when four letters picked without replacement from {g: 3, w: 1, h: 1, l: 1, a: 5}.
1/2640
Four letters picked without replacement from hkkkjokxkhhhk. Give prob of sequence hjhx.
1/1430
Two letters picked without replacement from fcffffffffcffcff. What is prob of sequence ff?
13/20
Two letters picked without replacement from pabppbpbpa. Give prob of sequence ba.
1/15
Calculate prob of sequence qhq when three letters picked without replacement from qhqqqhhhqqq.
28/165
Four letters picked without replacement from eeeyfeeyeyefeefeye. What is prob of sequence feey?
11/612
What is prob of sequence ww when two letters picked without replacement from ssww?
1/6
Two letters picked without replacement from vmv. What is prob of sequence mv?
1/3
Three letters picked without replacement from {f: 1, k: 1, p: 6, x: 8}. Give prob of sequence kpx.
1/70
Three letters picked without replacement from {v: 5, x: 6, p: 6, b: 1}. What is prob of sequence xpv?
5/136
Three letters picked without replacement from yygoyglgyyw. Give prob of sequence gwo.
1/330
What is prob of sequence rr when two letters picked without replacement from {w: 1, c: 5, r: 3, o: 1, h: 4, s: 1}?
1/35
Three letters picked without replacement from {f: 1, p: 1, a: 3}. What is prob of sequence afp?
1/20
Two letters picked without replacement from anoanohnn. What is prob of sequence no?
1/9
Three letters picked without replacement from cgpbbg. What is prob of sequence ggc?
1/60
What is prob of sequence lp when two letters picked without replacement from {a: 1, l: 2, w: 1, p: 2, q: 1, f: 1}?
1/14
Three letters picked without replacement from {p: 4, e: 8, v: 2}. Give prob of sequence vvp.
1/273
Three letters picked without replacement from vewyvweweeii. What is prob of sequence yvv?
1/660
Calculate prob of sequence lv when two letters picked without replacement from omolollvlsoooooos.
1/68
Three letters picked without replacement from nevvveeevevveeevevn. Give prob of sequence eev.
32/323
Two letters picked without replacement from {m: 7, d: 3}. Give prob of sequence mm.
7/15
Calculate prob of sequence spov when four letters picked without replacement from {s: 1, t: 1, v: 1, p: 1, o: 1}.
1/120
What is prob of sequence hxr when three letters picked without replacement from {f: 1, h: 1, a: 1, x: 1, l: 1, r: 2}?
1/105
Calculate prob of sequence rh when two letters picked without replacement from {h: 1, w: 1, b: 12, r: 1}.
1/210
Two letters picked without replacement from {w: 6, m: 3, t: 3, z: 1}. What is prob of sequence zm?
1/52
Calculate prob of sequence bb when two letters picked without replacement from azbbzbbyzyszzbzbbsss.
21/190
What is prob of sequence kiii when four letters picked without replacement from ikikkiiakkikikk?
8/273
Calculate prob of sequence bbi when three letters picked without replacement from ttitttjjttiijiibjbb.
5/969
What is prob of sequence wee when three letters picked without replacement from {w: 1, e: 2}?
1/3
Calculate prob of sequence kb when two letters picked without replacement from {d: 5, b: 1, x: 1, k: 1, f: 3}.
1/110
Three letters picked without replacement from tdtxdxtxdtdd. Give prob of sequence xxt.
1/55
Four letters picked without replacement from {y: 4, t: 6, z: 10}. Give prob of sequence tzyt.
10/969
Calculate prob of sequence ci when two letters picked without replacement from yciiciiciliiivlc.
2/15
What is prob of sequence in when two letters picked without replacement from ippispspkskissin?
1/60
What is prob of sequence psm when three letters picked without replacement from {y: 8, s: 4, p: 3, m: 2}?
1/170
Four letters picked without replacement from {p: 7, g: 3}. What is prob of sequence gppg?
1/20
Calculate prob of sequence hh when two letters picked without replacement from hthhethhethf.
5/22
What is prob of sequence mv when two letters picked without replacement from {v: 1, t: 3, m: 3}?
1/14
Four letters picked without replacement from {v: 5, g: 3}. Give prob of sequence ggvv.
1/14
Four letters picked without replacement from {h: 2, v: 2, f: 3, i: 1, d: 4}. What is prob of sequence fvih?
1/990
Calculate prob of sequence ckv when three letters picked without replacement from {z: 7, c: 1, k: 1, v: 3}.
1/440
What is prob of sequence fl when two letters picked without replacement from bflfbbfdabf?
2/55
What is prob of sequence wy when two letters picked without replacement from {c: 1, w: 2, s: 2, y: 3, l: 1, d: 6}?
1/35
Two letters picked without replacement from {v: 5, h: 8}. What is prob of sequence vv?
5/39
What is prob of sequence jt when two letters picked without replacement from {j: 1, d: 3, i: 1, t: 2}?
1/21
Two letters picked without replacement from {m: 1, l: 2, p: 1, s: 13, u: 1, b: 2}. Give prob of sequence bu.
1/190
Calculate prob of sequence ge when two letters picked without replacement from geegeegeggegg.
7/26
Calculate prob of sequence ats when three letters picked without replacement from {t: 5, s: 5, v: 3, a: 1, m: 1}.
5/546
What is prob of sequence xkx when three letters picked without replacement from {k: 4, h: 2, x: 7}?
14/143
Two letters picked without replacement from {x: 2, u: 2, o: 4, m: 5, k: 7}. Give prob of sequence xu.
1/95
Two letters picked without replacement from {g: 1, z: 9, y: 9}. What is prob of sequence yz?
9/38
Calculate prob of sequence zzd when three letters picked without replacement from zzdz.
1/4
Three letters picked without replacement from {j: 1, t: 1, h: 1}. What is prob of sequence jth?
1/6
Calculate prob of sequence uy when two letters picked without replacement from {l: 4, y: 2, u: 3}.
1/12
Calculate prob of sequence ltwy when four letters picked without replacement from {y: 1, t: 2, l: 4, e: 4, w: 8}.
2/2907
Calculate prob of sequence vvvv when four letters picked without replacement from {v: 8, o: 2}.
1/3
What is prob of sequence ng when two letters picked without replacement from {l: 2, c: 1, v: 1, n: 1, r: 1, g: 1}?
1/42
Four letters picked without replacement from {f: 9}. Give prob of sequence ffff.
1
What is prob of sequence oo when two letters picked without replacement from