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]


or of -133/66 and -47/111.
2442
What is the least common multiple of 57 and 12?
228
What is the lowest common multiple of 4656 and 18?
13968
Calculate the common denominator of 53/495 and -68/15.
495
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9000
What is the lowest common multiple of 88 and 110?
440
What is the least common multiple of 1856 and 2320?
9280
Calculate the common denominator of -31/154 and -31/66.
462
Calculate the least common multiple of 72 and 30.
360
Calculate the lowest common multiple of 4782 and 54.
43038
What is the smallest common multiple of 42 and 70?
210
Find the common denominator of -91/2328 and -71/388.
2328
What is the least common multiple of 1530 and 1870?
16830
Calculate the common denominator of -93/158 and -4/11.
1738
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225
Calculate the lowest common multiple of 44 and 156.
1716
What is the common denominator of -35/1622 and 89/18?
14598
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462
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113930
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1134
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264
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84
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112
Calculate the smallest common multiple of 32 and 260.
2080
Find the common denominator of 41/46 and -16/7.
322
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44
Find the common denominator of -61/2283 and 10.
2283
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3330
Calculate the smallest common multiple of 6 and 405.
810
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160
Calculate the common denominator of -40/301 and 11/11051.
77357
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1755
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1512
What is the least common multiple of 70 and 1120?
1120
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51136
Find the common denominator of -97/1110 and -83/15.
1110
Find the common denominator of 29/51 and -8/3.
51
Calculate the smallest common multiple of 7065 and 15.
7065
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1710
Find the common denominator of 74/3 and -59/51.
51
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18480
Calculate the common denominator of 19/7568 and -47/22.
7568
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308
Calculate the common denominator of 85/2272 and 25/48.
6816
Find the common denominator of 7/78 and -17/60.
780
Calculate the common denominator of 57/70 and -67/28.
140
Calculate the common denominator of 21/20 and 197/420.
420
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4074
Calculate the common denominator of -91/18 and -47/24.
72
Calculate the lowest common multiple of 60 and 642.
6420
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621
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2910
Calculate the common denominator of -7/15 and -17/105.
105
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6
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133
Calculate the lowest common multiple of 8 and 386.
1544
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3304
What is the common denominator of -23/336 and 47?
336
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12
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892
Calculate the common denominator of 87/16 and -71/44.
176
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7272
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4270
Calculate the smallest common multiple of 972 and 54.
972
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436
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280
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4576
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6480
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15
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198
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30
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28
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13622
Calculate the least common multiple of 5499 and 72.
43992
Calculate the smallest common multiple of 406 and 12.
2436
Calculate the common denominator of -83/32 and -83/84.
672
Calculate the smallest common multiple of 147222 and 2.
147222
Calculate the least common multiple of 171 and 159.
9063
Calculate the lowest common multiple of 81 and 1683.
15147
Find the common denominator of -63/22 and 63/1564.
17204
What is the smallest common multiple of 44 and 40?
440
Calculate the smallest common multiple of 112 and 10.
560
Calculate the common denominator of 125/54 and -103/1728.
1728
Calculate the lowest common multiple of 6 and 927.
1854
Find the common denominator of 15/16 and -145/1698.
13584
Calculate the common denominator of 123/20 and -103/378.
3780
What is the smallest common multiple of 48 and 16?
48
What is the lowest common multiple of 10 and 10?
10
What is the smallest common multiple of 84 and 84?
84
Find the common denominator of -13/627 and 29/24.
5016
What is the common denominator of 71/3333 and 46/3333?
3333
Calculate the smallest common multiple of 946 and 258.
2838
Find the common denominator of -109/18 and -139/2808.
2808
Find the common denominator of 49/596 and -93/22.
6556
What is the least common multiple of 4 and 134?
268
Calculate the smallest common multiple of 624 and 312.
624
What is the least common multiple of 123 and 12?
492
Calculate the least common multiple of 6 and 1731.
3462
Calculate the common denominator of 137/1800 and 37/18.
1800
Calculate the lowest common multiple of 25 and 625.
625
What is the least common multiple of 4778 and 22?
52558
Find the common denominator of -2 and 9/2.
2
What is the least common multiple of 63 and 2?
126
What is the common denominator of 61/1260 and -13/42?
1260
Calculate the common denominator of 123/10 and -109/1410.
1410
Calculate the lowest common multiple of 23 and 253.
253
Calculate the common denominator of -64/9 and 76/2211.
6633
Find the common denominator of -59/102 and 42/85.
510
Calculate the common denominator of 59/1666 and -5/98.
1666
What is the lowest common multiple of 42 and 21?
42
Calculate the common denominator of 53/12 and -85/44.
132
What is the least common multiple of 15 and 13?
195
Find the common denominator of -39/2 and -85/2774.
2774
Calculate the smallest common multiple of 5 and 5.
5
Calculate the least common multiple of 55 and 65.
715
Find the common denominator of 69/14 and -75/16.
112
Calculate the smallest common multiple of 16 and 624.
624
What is the least common multiple of 9 and 153?
153
What is the lowest common multiple of 5208 and 24?
5208
Find the common denominator of -47/100 and -71/1460.
7300
Calculate the common denominator of -79/48 and -59/42.
336
Calculate the lowest common multiple of 50 and 350.
350
Calculate the lowest common multiple of 204 and 818.
83436
Calculate the lowest common multiple of 80 and 10.
80
Calculate the lowest common multiple of 590 and 5428.
27140
What is the lowest common multiple of 10 and 52?
260
What is the common denominator of -7/90 and -149/90?
90
Find the common denominator of -107/70 and 107/140.
140
Calculate the common denominator of 83/812 and 21/464.
3248
Find the common denominator of -39/7634 and -77/6246.
68706
Calculate the smallest common multiple of 32 and 16.
32
Calculate the smallest common multiple of 616 and 396.
5544
Calculate the common denominator of 1/114 and -109/418.
1254
What is the common denominator of -53/48 and -97/132?
528
Find the common denominator of -22/939 and -62/33.
10329
Calculate the smallest common multiple of 9 and 345.
1035
Find the common denominator of 79/42 and 143/6804.
6804
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776
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2475
Find the common denominator of -26/55 and 71/2.
110
Find the common denominator of 51/8 and -101/1070.
4280
Calculate the common denominator of -77/4 and -10/1091.
4364
Calculate the lowest common multiple of 1218 and 161.
28014
Calculate the smallest common multiple of 1458 and 6.
1458
What is the common denominator of -39/308 and -13/21?
924
Calculate