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]


two letters picked without replacement from jgxnunxonxnn.
5/132
Two letters picked without replacement from nnnnnnnnnnnnlnnnnn. Give prob of sequence nl.
1/18
Calculate prob of sequence vb when two letters picked without replacement from wvwb.
1/12
What is prob of sequence zh when two letters picked without replacement from rztrthzzrhzrrhrth?
1/17
Calculate prob of sequence ud when two letters picked without replacement from {u: 2, d: 4}.
4/15
What is prob of sequence xi when two letters picked without replacement from {x: 2, p: 1, z: 1, i: 1}?
1/10
Three letters picked without replacement from oooooooooxoo. Give prob of sequence xoo.
1/12
What is prob of sequence ve when two letters picked without replacement from ovveevlevvllvlevll?
14/153
Calculate prob of sequence hpu when three letters picked without replacement from {r: 2, h: 2, u: 1, q: 1, p: 1}.
1/105
What is prob of sequence of when two letters picked without replacement from ndaddodfaqfffo?
4/91
Calculate prob of sequence ep when two letters picked without replacement from {p: 3, u: 1, g: 2, e: 4, y: 1}.
6/55
Two letters picked without replacement from {b: 2, a: 2, t: 2}. What is prob of sequence bt?
2/15
Two letters picked without replacement from osmor. Give prob of sequence rm.
1/20
Three letters picked without replacement from ymyymeyyypzmmyamyy. What is prob of sequence pey?
1/544
Two letters picked without replacement from ueueujjujeeuw. Give prob of sequence wj.
1/52
Two letters picked without replacement from {m: 1, r: 2}. What is prob of sequence rm?
1/3
Three letters picked without replacement from {k: 1, i: 3, g: 3}. Give prob of sequence igk.
3/70
Three letters picked without replacement from {x: 10}. Give prob of sequence xxx.
1
Two letters picked without replacement from qizzqqzqqqqozqzzq. What is prob of sequence oz?
3/136
Four letters picked without replacement from izviizzvkkiik. What is prob of sequence zzzk?
3/2860
What is prob of sequence aja when three letters picked without replacement from {j: 5, a: 2, n: 3, z: 3}?
5/858
Two letters picked without replacement from jhgaapapjbgbpa. What is prob of sequence ah?
2/91
Three letters picked without replacement from lbbllbkklylbl. Give prob of sequence kbb.
2/143
Two letters picked without replacement from tzutmuuutupttuupt. What is prob of sequence mp?
1/136
Four letters picked without replacement from {z: 2, j: 2, u: 11}. Give prob of sequence uzjj.
11/8190
Three letters picked without replacement from {i: 1, x: 1, u: 4, m: 5}. What is prob of sequence mum?
8/99
Two letters picked without replacement from rrjccrrjccczqrrjqqr. What is prob of sequence rr?
7/57
Calculate prob of sequence vn when two letters picked without replacement from {r: 1, t: 1, d: 1, v: 1, n: 1}.
1/20
Two letters picked without replacement from {j: 4, s: 4, x: 1, a: 3, e: 2}. What is prob of sequence ae?
3/91
Four letters picked without replacement from {x: 2, s: 3, y: 5, n: 3}. What is prob of sequence snxx?
3/2860
Two letters picked without replacement from {t: 3, v: 4, w: 1, n: 2, x: 8, j: 2}. What is prob of sequence wn?
1/190
Three letters picked without replacement from bbibbiiibibbiibb. What is prob of sequence ibi?
9/80
Four letters picked without replacement from zzyffyvyyfyy. What is prob of sequence fvzz?
1/1980
Calculate prob of sequence pbxp when four letters picked without replacement from ppgbbgbghbxgbx.
5/6006
Two letters picked without replacement from {b: 2, j: 1, w: 2, e: 1, o: 1}. What is prob of sequence we?
1/21
Three letters picked without replacement from zzmbgmbmbzmvmbzbmb. What is prob of sequence vbz?
1/204
Four letters picked without replacement from {w: 5, m: 2}. Give prob of sequence mmww.
1/21
Two letters picked without replacement from {s: 3, b: 13, t: 2}. Give prob of sequence bt.
13/153
What is prob of sequence fpf when three letters picked without replacement from {p: 4, t: 7, f: 5, c: 2}?
5/306
What is prob of sequence ssl when three letters picked without replacement from lsslsl?
3/20
What is prob of sequence ue when two letters picked without replacement from ueeueueueuuueueu?
21/80
Two letters picked without replacement from {h: 5, a: 2, k: 5}. What is prob of sequence ha?
5/66
What is prob of sequence nnnn when four letters picked without replacement from jnji?
0
What is prob of sequence xj when two letters picked without replacement from xsjsjjs?
1/14
What is prob of sequence aaa when three letters picked without replacement from rrrarraraaarrrrr?
1/56
Calculate prob of sequence jw when two letters picked without replacement from tttjwjttttttttttt.
1/136
Calculate prob of sequence kk when two letters picked without replacement from kdkkjdhkdhkvk.
5/26
What is prob of sequence cr when two letters picked without replacement from rccrgcnragr?
6/55
Calculate prob of sequence nz when two letters picked without replacement from iizeinziiinznziiiz.
5/102
Two letters picked without replacement from yjjjjjjjlyldolljjll. What is prob of sequence ld?
1/57
What is prob of sequence vvsf when four letters picked without replacement from smiffvvpi?
1/756
Calculate prob of sequence rrxr when four letters picked without replacement from woxrxxwworwwwxr.
1/1365
Calculate prob of sequence zljn when four letters picked without replacement from lpznsnjnsjnj.
1/990
What is prob of sequence vwv when three letters picked without replacement from {v: 7, w: 5}?
7/44
Three letters picked without replacement from jkeojpj. Give prob of sequence jje.
1/35
What is prob of sequence iii when three letters picked without replacement from iiiiiiiiissiisiiiisi?
28/57
Four letters picked without replacement from zzzznzznnznn. Give prob of sequence nnnz.
7/198
Calculate prob of sequence atr when three letters picked without replacement from {e: 4, a: 3, t: 7, r: 3, x: 1}.
7/544
What is prob of sequence izzz when four letters picked without replacement from zizziiz?
3/35
Three letters picked without replacement from keeeavavae. Give prob of sequence eka.
1/60
What is prob of sequence jv when two letters picked without replacement from {v: 1, j: 2}?
1/3
Two letters picked without replacement from {v: 4, y: 3, s: 1, o: 6, j: 4, z: 2}. What is prob of sequence os?
3/190
Two letters picked without replacement from yjeyyvyev. What is prob of sequence ey?
1/9
Three letters picked without replacement from pgp. Give prob of sequence pgp.
1/3
Four letters picked without replacement from {s: 8, k: 2}. What is prob of sequence ssss?
1/3
Two letters picked without replacement from {v: 1, p: 3, j: 1, h: 1, r: 1}. What is prob of sequence rv?
1/42
Three letters picked without replacement from hmtgm. Give prob of sequence mmg.
1/30
Two letters picked without replacement from {v: 1, u: 5, g: 4}. Give prob of sequence vg.
2/45
Calculate prob of sequence qzzz when four letters picked without replacement from {z: 6, q: 7}.
7/143
Two letters picked without replacement from eqeqee. What is prob of sequence qq?
1/15
Calculate prob of sequence hdh when three letters picked without replacement from ihguudguuugihhx.
1/455
Two letters picked without replacement from {e: 3, c: 1, m: 5, u: 1, y: 1}. Give prob of sequence cy.
1/110
Three letters picked without replacement from {m: 2, z: 2, f: 3, n: 4}. What is prob of sequence zmn?
8/495
Two letters picked without replacement from wwwowwwwwowsssyw. What is prob of sequence sw?
1/8
Four letters picked without replacement from {q: 1, j: 2, f: 1, e: 2, p: 1, h: 1}. What is prob of sequence jhpq?
1/840
Calculate prob of sequence am when two letters picked without replacement from {l: 1, a: 2, m: 1, v: 3}.
1/21
Three letters picked without replacement from {v: 1, p: 1, y: 1, x: 1, q: 1, w: 2}. What is prob of sequence vqw?
1/105
Three letters picked without replacement from {g: 3, y: 4}. Give prob of sequence gyg.
4/35
Two letters picked without replacement from hxxxxxxxhxxhhx. Give prob of sequence hx.
20/91
What is prob of sequence oc when two letters picked without replacement from {c: 4, q: 1, o: 2, d: 3, t: 4}?
4/91
Calculate prob of sequence fjf when three letters picked without replacement from {y: 1, j: 4, f: 5}.
1/9
Calculate prob of sequence gww when three letters picked without replacement from vwgggvvgwvvv.
1/