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]


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35/228
What is prob of sequence uu when two letters picked without replacement from {l: 2, m: 4, u: 3}?
1/12
Two letters picked without replacement from eeogi. Give prob of sequence oe.
1/10
Three letters picked without replacement from {i: 5, x: 3}. What is prob of sequence xii?
5/28
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1/60
Calculate prob of sequence ppv when three letters picked without replacement from vprvppvpvrprvvp.
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Calculate prob of sequence cjyw when four letters picked without replacement from jcacajcawcwaays.
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Four letters picked without replacement from {z: 6, p: 4, l: 3}. What is prob of sequence lpzz?
3/143
Two letters picked without replacement from {e: 2, d: 11}. What is prob of sequence ee?
1/78
Calculate prob of sequence vv when two letters picked without replacement from vavaaav.
1/7
What is prob of sequence tdg when three letters picked without replacement from {y: 2, g: 1, t: 2, d: 1}?
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Calculate prob of sequence hq when two letters picked without replacement from {l: 1, z: 2, v: 3, h: 2, g: 2, q: 4}.
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What is prob of sequence fqf when three letters picked without replacement from {t: 2, q: 9, f: 7}?
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Three letters picked without replacement from sdddrsrdsddds. Give prob of sequence srr.
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Four letters picked without replacement from {z: 2, f: 8}. Give prob of sequence zzff.
1/45
Two letters picked without replacement from {e: 19, j: 1}. What is prob of sequence ee?
9/10
Calculate prob of sequence du when two letters picked without replacement from {u: 3, k: 6, d: 2, q: 3, w: 6}.
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Three letters picked without replacement from iilifiiiffftftlftl. Give prob of sequence fif.
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Calculate prob of sequence hb when two letters picked without replacement from {t: 4, v: 3, s: 4, b: 3, h: 2, k: 2}.
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Three letters picked without replacement from {r: 2, i: 2, y: 2, m: 1, a: 1, b: 7}. Give prob of sequence bmi.
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Four letters picked without replacement from ozogoszzozgzzgzo. What is prob of sequence ogoo?
3/728
Two letters picked without replacement from uuuuuiuuuuuuuuu. What is prob of sequence ii?
0
Two letters picked without replacement from {u: 1, i: 1, s: 1}. What is prob of sequence si?
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Four letters picked without replacement from {o: 7, y: 4, h: 2}. Give prob of sequence oohh.
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Four letters picked without replacement from loonlvnnzvbonol. Give prob of sequence nolo.
2/455
What is prob of sequence wt when two letters picked without replacement from ttottttwowoow?
3/26
What is prob of sequence sssm when four letters picked without replacement from msttttatctttsstcscct?
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Calculate prob of sequence kp when two letters picked without replacement from ckbkpzcccc.
1/45
Calculate prob of sequence wxg when three letters picked without replacement from {g: 2, t: 7, w: 4, x: 1}.
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Two letters picked without replacement from jaiijajjeijjaiiij. What is prob of sequence ae?
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What is prob of sequence kc when two letters picked without replacement from kilddkdckc?
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Three letters picked without replacement from {e: 16, r: 2}. Give prob of sequence eer.
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What is prob of sequence lf when two letters picked without replacement from {f: 4, l: 3, a: 9}?
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What is prob of sequence uh when two letters picked without replacement from uuhuhhhhuhh?
14/55
Three letters picked without replacement from {r: 3, s: 6, z: 1, d: 4}. What is prob of sequence sdd?
3/91
Three letters picked without replacement from wwwuwwwwwwwuw. What is prob of sequence wwu?
5/39
Calculate prob of sequence ehu when three letters picked without replacement from esjuihs.
1/210
Three letters picked without replacement from {j: 5}. What is prob of sequence jjj?
1
Four letters picked without replacement from {q: 1, z: 2, u: 3, m: 1, t: 3, o: 1}. What is prob of sequence ztuo?
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What is prob of sequence tj when two letters picked without replacement from tejvy?
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Calculate prob of sequence re when two letters picked without replacement from {r: 1, q: 1, e: 16}.
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Four letters picked without replacement from dnnoggq. Give prob of sequence odnq.
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What is prob of sequence gb when two letters picked without replacement from {c: 3, b: 6, n: 1, d: 1, g: 1, t: 1}?
1/26
Two letters picked without replacement from {h: 1, o: 1, l: 8, g: 1, v: 4, i: 1}. What is prob of sequence ll?
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What is prob of sequence hll when three letters picked without replacement from hlrll?
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What is prob of sequence ggff when four letters picked without replacement from ffuufoffuffgufgfugof?
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What is prob of sequence nnn when three letters picked without replacement from {n: 3, a: 1, q: 1}?
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What is prob of sequence mdd when three letters picked without replacement from ymmtbydddy?
1/60
Calculate prob of sequence uubt when four letters picked without replacement from {v: 5, u: 3, t: 2, b: 3}.
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What is prob of sequence yz when two letters picked without replacement from ggeyszz?
1/21
Calculate prob of sequence ps when two letters picked without replacement from {x: 3, p: 1, a: 4, u: 2, s: 1}.
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Three letters picked without replacement from {t: 1, c: 4, f: 4, q: 2, l: 5}. What is prob of sequence lqf?
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Four letters picked without replacement from dfxdzxfdffzqq. Give prob of sequence fzfq.
2/715
Three letters picked without replacement from nneeuunnekexkenexe. What is prob of sequence knu?
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What is prob of sequence rfr when three letters picked without replacement from {u: 1, f: 1, r: 3}?
1/10
Three letters picked without replacement from sudusndujssussx. What is prob of sequence sdd?
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Calculate prob of sequence nn when two letters picked without replacement from nntuuunutuqrtqq.
1/35
What is prob of sequence jss when three letters picked without replacement from ssjsvvv?
1/35
What is prob of sequence af when two letters picked without replacement from ffbffoffffbffabbbabo?
1/19
Calculate prob of sequence pdd when three letters picked without replacement from {w: 10, d: 6, p: 1}.
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What is prob of sequence jnj when three letters picked without replacement from {x: 6, e: 2, o: 3, v: 5, j: 3, n: 1}?
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What is prob of sequence ws when two letters picked without replacement from owwochchsocwchwwhhlc?
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Two letters picked without replacement from {o: 2, b: 3}. What is prob of sequence ob?
3/10
Four letters picked without replacement from {j: 2, w: 2, l: 4, s: 1, g: 1, m: 2}. Give prob of sequence wlsj.
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Calculate prob of sequence efp when three letters picked without replacement from {p: 2, f: 2, e: 2, q: 3}.
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Calculate prob of sequence vf when two letters picked without replacement from ffffgsfgvgfvgzg.
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Four letters picked without replacement from ffdllv. What is prob of sequence lvlf?
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Calculate prob of sequence jjju when four letters picked without replacement from jjjjujuj.
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Two letters picked without replacement from zooosfsasf. Give prob of sequence oa.
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Calculate prob of sequence nuu when three letters picked without replacement from {n: 5, e: 1, u: 4, a: 1}.
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Three letters picked without replacement from lnalap. Give prob of sequence nll.
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Three letters picked without replacement from ppppp. What is prob of sequence ppp?
1
What is prob of sequence fkf when three letters picked without replacement from {k: 3, b: 5, h: 6, f: 2, p: 1}?
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Calculate prob of sequence qc when two letters picked without replacement from jjnjqnjqjjqcqcjj.
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Three letters picked without replacement from kmkkgkkkgkgggkko. Give prob of sequence kko.
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Calculate prob of sequence bx when two letters picked without replacement from sxsbhmq.
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Four letters picked without replacement from xqqykybykbyry. What is prob of sequence bkky?
1/858
Three letters picked without replacement from {y: 3, h: 4}. What is prob of sequence hhy?
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Four letters picked without replacement from ajajracas. What is prob of sequence aarr?
0
Four letters picked without replacement from {a: 3, v: 3, m: 2}. Give prob of sequence vmmv.
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Calculate prob of sequence wfw when three letters picked without replacement from jjjjwjwwjjfjwfw.
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Four letters picked without replacement from {n: 3, w: 2}. What is p