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]


1}.
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What is prob of sequence kkn when three letters picked without replacement from {k: 10, n: 1, r: 3, q: 5, e: 1}?
1/76
Three letters picked without replacement from hlxkqkk. Give prob of sequence xkq.
1/70
Two letters picked without replacement from {b: 2, i: 2, g: 10}. Give prob of sequence bb.
1/91
Two letters picked without replacement from {o: 1, s: 4, b: 2, c: 4}. What is prob of sequence bs?
4/55
Calculate prob of sequence bhzb when four letters picked without replacement from hhbbzhb.
3/140
Two letters picked without replacement from reqrrwqrqr. Give prob of sequence ew.
1/90
Calculate prob of sequence ks when two letters picked without replacement from jzeqssk.
1/21
What is prob of sequence lmm when three letters picked without replacement from mllmlllm?
5/56
Calculate prob of sequence lnrr when four letters picked without replacement from {l: 5, z: 6, x: 1, n: 5, r: 2}.
25/46512
What is prob of sequence xxx when three letters picked without replacement from xxx?
1
Three letters picked without replacement from ppxpppxp. Give prob of sequence ppx.
5/28
Four letters picked without replacement from kakkkmmek. Give prob of sequence kkkm.
5/126
What is prob of sequence mjm when three letters picked without replacement from {m: 2, j: 10}?
1/66
Four letters picked without replacement from dkrytrrtrdrny. What is prob of sequence knty?
1/4290
Calculate prob of sequence xx when two letters picked without replacement from {r: 4, k: 8, x: 4}.
1/20
What is prob of sequence xv when two letters picked without replacement from {x: 2, k: 1, y: 2, v: 1}?
1/15
Two letters picked without replacement from {u: 1, r: 5, z: 1, x: 10}. What is prob of sequence zx?
5/136
What is prob of sequence mmi when three letters picked without replacement from {s: 5, m: 4, i: 1, u: 1}?
2/165
Three letters picked without replacement from {u: 3, o: 3, x: 2, r: 1, v: 1, k: 1}. What is prob of sequence vku?
1/330
Calculate prob of sequence of when two letters picked without replacement from {o: 1, k: 1, f: 1, s: 2}.
1/20
Four letters picked without replacement from tcrresg. Give prob of sequence creg.
1/420
Calculate prob of sequence ooo when three letters picked without replacement from {m: 1, o: 6, s: 3, i: 3}.
10/143
Calculate prob of sequence bfbp when four letters picked without replacement from {f: 9, p: 2, b: 5}.
3/364
What is prob of sequence rcrb when four letters picked without replacement from bcccrrrcc?
5/504
Two letters picked without replacement from {i: 2, k: 5}. Give prob of sequence kk.
10/21
Two letters picked without replacement from ooenennooooeooooooo. What is prob of sequence nn?
1/57
Calculate prob of sequence gq when two letters picked without replacement from qgbgqlqqgqd.
3/22
Two letters picked without replacement from {e: 1, p: 1, l: 1, b: 1, q: 2, v: 1}. What is prob of sequence vl?
1/42
Three letters picked without replacement from tqqjt. Give prob of sequence tjt.
1/30
Three letters picked without replacement from {v: 5, r: 2, i: 5}. What is prob of sequence vvv?
1/22
Two letters picked without replacement from izdzdbdzekdziik. What is prob of sequence ze?
2/105
Two letters picked without replacement from {v: 1, h: 3, s: 1}. Give prob of sequence sv.
1/20
Two letters picked without replacement from aaaaaaaaaa. What is prob of sequence aa?
1
What is prob of sequence nlt when three letters picked without replacement from {n: 1, e: 1, t: 1, a: 5, l: 1}?
1/504
Three letters picked without replacement from {g: 5, q: 3, j: 2}. What is prob of sequence jjq?
1/120
Calculate prob of sequence vyk when three letters picked without replacement from ktnykvtiyktytkkkin.
1/272
Three letters picked without replacement from {p: 8, t: 4, o: 1, e: 4, i: 1, x: 2}. What is prob of sequence oxp?
2/855
Two letters picked without replacement from {n: 12, l: 1}. What is prob of sequence nn?
11/13
Calculate prob of sequence hrh when three letters picked without replacement from {r: 1, i: 5, h: 11}.
11/408
Calculate prob of sequence jjj when three letters picked without replacement from jjjjjjjjj.
1
Calculate prob of sequence xxj when three letters picked without replacement from jxjjjxjjjjjxjx.
5/91
Four letters picked without replacement from qqzsgqsq. Give prob of sequence qqsz.
1/70
Two letters picked without replacement from uawwwmnnnaana. Give prob of sequence mw.
1/52
Two letters picked without replacement from {t: 2, h: 5, y: 3, a: 8, s: 2}. Give prob of sequence yy.
3/190
Two letters picked without replacement from {c: 6, l: 1, g: 7}. Give prob of sequence lg.
1/26
What is prob of sequence jp when two letters picked without replacement from jttptjttjjpt?
2/33
What is prob of sequence ppii when four letters picked without replacement from {d: 2, i: 4, p: 4}?
1/35
Calculate prob of sequence fb when two letters picked without replacement from fdkbt.
1/20
What is prob of sequence et when two letters picked without replacement from set?
1/6
Two letters picked without replacement from {k: 3, v: 5, m: 1, t: 1, n: 1, b: 1}. Give prob of sequence nv.
5/132
Three letters picked without replacement from {t: 1, u: 2, g: 1, l: 4, v: 1, c: 3}. Give prob of sequence cvg.
1/440
Three letters picked without replacement from mtmenttvt. What is prob of sequence vmt?
1/63
Calculate prob of sequence wtt when three letters picked without replacement from {f: 2, a: 1, x: 2, m: 3, t: 3, w: 1}.
1/220
Four letters picked without replacement from {p: 3, x: 6, t: 3, n: 3}. What is prob of sequence xxxt?
1/91
Four letters picked without replacement from vvyvalvivtytlvillvv. What is prob of sequence yiil?
1/5814
Four letters picked without replacement from ojcoeoj. What is prob of sequence jeco?
1/140
What is prob of sequence dctt when four letters picked without replacement from {t: 4, d: 1, m: 1, e: 1, c: 2}?
1/126
What is prob of sequence jh when two letters picked without replacement from hjhhahhhhjjhjh?
18/91
Four letters picked without replacement from nwpnpnnp. Give prob of sequence pnpn.
3/70
Four letters picked without replacement from {v: 4, d: 1, o: 2, a: 1, n: 2}. What is prob of sequence adnn?
1/2520
Two letters picked without replacement from mgolp. What is prob of sequence go?
1/20
Calculate prob of sequence irr when three letters picked without replacement from wirccwirrrrrcip.
3/91
Three letters picked without replacement from {b: 1, j: 4, a: 1, s: 4}. What is prob of sequence abs?
1/180
Three letters picked without replacement from {v: 2, a: 1}. Give prob of sequence avv.
1/3
Four letters picked without replacement from diidddddd. What is prob of sequence ddii?
1/36
Two letters picked without replacement from {k: 1, r: 2, q: 1, b: 3}. What is prob of sequence kr?
1/21
Two letters picked without replacement from aucvagc. Give prob of sequence cv.
1/21
What is prob of sequence rccr when four letters picked without replacement from cccrrcrcccccccrcrc?
13/306
What is prob of sequence kg when two letters picked without replacement from {m: 2, k: 1, f: 1, t: 2, g: 1, l: 1}?
1/56
Calculate prob of sequence nnu when three letters picked without replacement from nunn.
1/4
Four letters picked without replacement from jdjffjjjf. Give prob of sequence fjdf.
5/504
Three letters picked without replacement from {i: 1, y: 1, m: 9}. What is prob of sequence mim?
4/55
Calculate prob of sequence yyaq when four letters picked without replacement from jpqyyqqqyaqjqpjy.
3/1820
Two letters picked without replacement from {b: 2, x: 3}. What is prob of sequence xx?
3/10
What is prob of sequence ws when two letters picked without replacement from {w: 2, s: 1, b: 2, x: 1, t: 1}?
1/21
Two letters picked without replacement from {g: 1, d: 12, z: 1, j: 2, w: 2}. What is prob of sequence dj?
4/51
Four letters picked without replacement from kdkczcckdckkvkrc. Give prob of sequence vzcr.
1/8736
Two letters picked without replacement from {x: 1, e: 1, y: 1, w: 5, o: 4}. What is prob of sequence ow?
5/33
Calculate prob of sequence dnsd when four letters picked without replacement from oojsdsndsnsononinnnn.
8/14535
What is prob of sequence aa when two letters picked without replacement from {b: 2, a: 11, y: 1}?
55/91
Calculate prob of sequence xi when two letters picked without replacement from ojxjrx