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]


without replacement from {b: 1, r: 1, q: 2, w: 1}.
1/10
What is prob of sequence fm when two letters picked without replacement from {f: 1, d: 2, m: 1, p: 1}?
1/20
Calculate prob of sequence git when three letters picked without replacement from {t: 1, y: 2, i: 1, k: 2, g: 2}.
1/168
What is prob of sequence kp when two letters picked without replacement from fpkfckfpkpcpc?
1/13
Two letters picked without replacement from {u: 3, h: 17}. Give prob of sequence hh.
68/95
Four letters picked without replacement from {d: 1, s: 4, r: 5, y: 5}. What is prob of sequence sssd?
1/1365
What is prob of sequence wq when two letters picked without replacement from lzqfqlzfqlzwzqdqdqd?
1/57
What is prob of sequence ij when two letters picked without replacement from {j: 2, b: 2, t: 1, i: 1, d: 2, u: 1}?
1/36
Two letters picked without replacement from {c: 6, k: 5, o: 1, q: 1, l: 2}. Give prob of sequence cl.
2/35
Calculate prob of sequence yyyy when four letters picked without replacement from {y: 5}.
1
Two letters picked without replacement from {q: 2, e: 2, g: 5, z: 2, h: 2}. Give prob of sequence hz.
1/39
Four letters picked without replacement from pbfeewehefpb. Give prob of sequence fwef.
1/1485
Calculate prob of sequence llu when three letters picked without replacement from {u: 5, l: 11}.
55/336
Four letters picked without replacement from {v: 6, x: 6, l: 1, h: 5, q: 1}. What is prob of sequence lxxq?
5/15504
What is prob of sequence lt when two letters picked without replacement from tppmmlltppt?
3/55
Three letters picked without replacement from joos. Give prob of sequence oso.
1/12
Calculate prob of sequence sao when three letters picked without replacement from {s: 13, o: 2, a: 2, i: 3}.
13/1710
Four letters picked without replacement from {j: 9, m: 3}. Give prob of sequence jmjm.
2/55
Four letters picked without replacement from gllgllgllgggg. What is prob of sequence glll?
7/143
What is prob of sequence uggl when four letters picked without replacement from luggsgu?
1/70
Two letters picked without replacement from kkdkkkkkkkkkkkk. What is prob of sequence kk?
13/15
Four letters picked without replacement from {d: 3, k: 9, i: 4}. Give prob of sequence ikdk.
9/455
Two letters picked without replacement from bbbbbb. What is prob of sequence bb?
1
Four letters picked without replacement from {g: 2, a: 2, i: 1, t: 1, v: 2}. What is prob of sequence agti?
1/420
Four letters picked without replacement from {q: 2, l: 2, g: 3, n: 2}. What is prob of sequence qqgn?
1/252
Four letters picked without replacement from {y: 5, w: 8}. What is prob of sequence wyww?
14/143
What is prob of sequence jj when two letters picked without replacement from {j: 11, r: 1}?
5/6
Two letters picked without replacement from {v: 1, o: 17}. Give prob of sequence vo.
1/18
Three letters picked without replacement from zyiygjyzjymmy. Give prob of sequence imj.
1/429
Three letters picked without replacement from {g: 4, b: 1, k: 4, a: 2, l: 6}. What is prob of sequence bgk?
1/255
Calculate prob of sequence uuo when three letters picked without replacement from {u: 5, m: 8, o: 3}.
1/56
Three letters picked without replacement from {d: 1, o: 1, h: 2}. Give prob of sequence ohd.
1/12
Four letters picked without replacement from {k: 3, s: 3}. What is prob of sequence kkss?
1/10
Calculate prob of sequence cv when two letters picked without replacement from ecvxvbgb.
1/28
Calculate prob of sequence zb when two letters picked without replacement from {z: 1, w: 1, v: 5, b: 2, e: 8}.
1/136
Calculate prob of sequence rkkk when four letters picked without replacement from ruurkkkqkr.
1/70
Calculate prob of sequence zi when two letters picked without replacement from hiihiihihiihhiziz.
9/136
What is prob of sequence kvdd when four letters picked without replacement from vdtdvkddkt?
1/105
What is prob of sequence bq when two letters picked without replacement from {s: 1, o: 6, b: 9, q: 2}?
1/17
Calculate prob of sequence rv when two letters picked without replacement from hrrv.
1/6
Two letters picked without replacement from pxxxs. Give prob of sequence sp.
1/20
What is prob of sequence lg when two letters picked without replacement from {u: 1, m: 1, e: 2, v: 1, l: 1, g: 1}?
1/42
Calculate prob of sequence uhpp when four letters picked without replacement from {b: 3, p: 5, u: 1, h: 1}.
1/252
Calculate prob of sequence vvsv when four letters picked without replacement from {f: 1, s: 2, v: 1}.
0
What is prob of sequence obo when three letters picked without replacement from {c: 3, p: 3, b: 8, o: 2}?
1/210
Four letters picked without replacement from {a: 4, s: 4, c: 3}. What is prob of sequence asas?
1/55
Calculate prob of sequence kmi when three letters picked without replacement from kmmhkkskkkkkhsi.
8/1365
What is prob of sequence rfr when three letters picked without replacement from gggggrgfgrwggffg?
1/560
Four letters picked without replacement from siifdtdfpsipti. Give prob of sequence dids.
2/3003
Two letters picked without replacement from qdzdl. Give prob of sequence ld.
1/10
Calculate prob of sequence hj when two letters picked without replacement from mmdjddzhjgj.
3/110
Three letters picked without replacement from {y: 1, h: 4, l: 3}. What is prob of sequence hhl?
3/28
Four letters picked without replacement from eeeqeqqe. Give prob of sequence qeqe.
1/14
What is prob of sequence kikk when four letters picked without replacement from {i: 2, k: 4}?
2/15
Calculate prob of sequence gqw when three letters picked without replacement from {w: 2, q: 1, g: 9, k: 1, d: 4}.
3/680
What is prob of sequence jmj when three letters picked without replacement from {q: 2, u: 1, j: 5, g: 1, m: 1}?
1/36
Three letters picked without replacement from {n: 2, w: 3, v: 3}. What is prob of sequence vww?
3/56
Two letters picked without replacement from {u: 2, i: 3, x: 1, s: 1}. What is prob of sequence xu?
1/21
Calculate prob of sequence aat when three letters picked without replacement from aatasjtjsttjs.
2/143
Three letters picked without replacement from qumuuuuuauuuuuam. Give prob of sequence uqu.
11/336
Two letters picked without replacement from {i: 2, d: 2, b: 2, t: 2}. Give prob of sequence tt.
1/28
Four letters picked without replacement from {m: 2, v: 9, h: 2}. Give prob of sequence mhmh.
1/4290
Four letters picked without replacement from xwxuunxwxxx. Give prob of sequence xwnu.
1/330
Three letters picked without replacement from zwwwzzuuux. What is prob of sequence www?
1/120
What is prob of sequence sslm when four letters picked without replacement from {t: 1, s: 3, q: 3, m: 4, l: 6, p: 2}?
1/646
Two letters picked without replacement from {t: 1, l: 1, d: 1, x: 1, a: 1}. What is prob of sequence dl?
1/20
Two letters picked without replacement from kolkv. Give prob of sequence vl.
1/20
What is prob of sequence rrrr when four letters picked without replacement from rrrrrrrrrr?
1
What is prob of sequence hq when two letters picked without replacement from {m: 1, u: 1, q: 5, h: 3, w: 1}?
3/22
What is prob of sequence blll when four letters picked without replacement from {l: 8, p: 3, b: 7}?
49/1530
What is prob of sequence on when two letters picked without replacement from aoguunboobb?
3/110
Four letters picked without replacement from {k: 3, l: 1, x: 3, r: 6, w: 1}. Give prob of sequence kxrl.
9/4004
Calculate prob of sequence esm when three letters picked without replacement from ssessssms.
1/72
What is prob of sequence mdt when three letters picked without replacement from {c: 4, m: 2, t: 1, d: 2, g: 1}?
1/180
Calculate prob of sequence jkj when three letters picked without replacement from {k: 2, j: 16}.
5/51
What is prob of sequence caft when four letters picked without replacement from {t: 1, f: 1, c: 3, x: 2, a: 5}?
1/792
Three letters picked without replacement from {u: 1, j: 4, k: 3}. Give prob of sequence ukk.
1/56
Two letters picked without replacement from jblljqmljb. What is prob of sequence jm?
1/30
What is prob of sequence isz when three letters picked without replacement from uzwsiusss?
1/126
Four letters picked without replacement from qqqwqwqq. Give prob of sequence qqwq.
1/7
Two letters picked without replacement from xaaxaxraxxrarakaxa. Give prob of sequence aa.
28/153
Two lette