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]


e of 14628 and 276?
14628
What is the smallest common multiple of 37286 and 1991?
410146
Find the common denominator of -58/7059 and -13/2715.
35295
Calculate the common denominator of -46/2129 and 51/5.
10645
Calculate the smallest common multiple of 1314 and 39420.
39420
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41661
What is the smallest common multiple of 10368 and 64?
10368
Find the common denominator of -93/968 and -85/12848.
141328
Find the common denominator of 29/3120 and 1/61386.
2455440
Find the common denominator of -35/266192 and 71/30480.
3992880
Calculate the common denominator of -58/19585 and 39/992.
19428320
Find the common denominator of 11/119928 and 59/21.
839496
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43660
Calculate the common denominator of 109/9920 and -97/44.
109120
Calculate the common denominator of -32/189567 and -73/34.
379134
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2968
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1388016
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227217
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17802
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33060
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4182
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724668
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510601
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891252
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10004456
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41306
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14430
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1080508
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51720
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421632
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62244
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1420578
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38248
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31320
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192080
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67760
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6642
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6045
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5796
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138936
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864
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107190
Calculate the common denominator of -73/8 and 21/2678.
10712
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8367996
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241020
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201552
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4478712
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478950
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7020
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834444
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384090
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762620
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106204
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15087450
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787138
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30705
Calculate the lowest common multiple of 58 and 649455.
1298910
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160104
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359892
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4133754
Find the common denominator of -23/5510 and 71/342.
49590
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549432
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153168
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4024020
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1304820
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20385
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17720
Calculate the least common multiple of 86 and 16645.
1431470
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2736
Calculate the common denominator of -61/9006 and 87/6004.
18012
Calculate the smallest common multiple of 9174 and 198.
27522
What is the common denominator of 95/1152 and 71/936?
14976
Calculate the least common multiple of 474 and 1394.
330378
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19392
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245050
Find the common denominator of -83/26314 and 151/29436.
1736724
Calculate the common denominator of -31/13654 and 75/4.
27308
What is the common denominator of -67/1848 and -25/1452?
20328
Find the common denominator of -68/12963 and 54/551.
246297
What is the least common multiple of 31 and 638?
19778
What is the common denominator of -43/1832 and -52/11679?
93432
What is the common denominator of 65/13548 and -127/12?
13548
Calculate the lowest common multiple of 2142 and 94.
100674
Calculate the lowest common multiple of 13878 and 6.
13878
What is the common denominator of -3/32488 and 127/36680?
1137080
Calculate the lowest common multiple of 310 and 42284.
211420
What is the lowest common multiple of 515 and 2745?
282735
What is the common denominator of -157/612 and -61/24?
1224
What is the lowest common multiple of 375224 and 220720?
3752240
Find the common denominator of -1/5797 and -25/6.
34782
Calculate the common denominator of -7/22 and 85/38326.
421586
What is the least common multiple of 248989 and 11128?
1991912
Calculate the least common multiple of 484610 and 6440.
1938440
Calculate the smallest common multiple of 1922 and 38440.
38440
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857504
What is the common denominator of -3/13472 and 79/40416?
40416
Calculate the least common multiple of 221884 and 286.
2440724
Calculate the smallest common multiple of 8424 and 17928.
699192
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94150
Calculate the lowest common multiple of 10460 and 596220.
596220
Find the common denominator of 41/24 and -73/1412.
8472
What is the common denominator of -13/746 and -33/41?
30586
What is the lowest common multiple of 53760 and 2520?
161280
What is the least common multiple of 2046060 and 11?
22506660
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2799
What is the common denominator of -57/9950 and 81/10?
9950
What is the common denominator of -15/21781 and 85/8?
174248
Calculate the least common multiple of 21114 and 3.
21114
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620724
What is the smallest common multiple of 235590 and 6?
235590
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36400
What is the smallest common multiple of 87 and 10080?
292320
What is the lowest common multiple of 79884 and 22824?
159768
What is the lowest common multiple of 1732 and 1620?
701460
Find the common denominator of 53/2570 and 73/3540.
909780
Calculate the least common multiple of 8792 and 42704.
298928
What is the least common multiple of 280 and 1820?
3640
What is the lowest common multiple of 729 and 3888?
11664
What is the common denominator of -99/78392 and -39/109940?
9015080
Calculate the lowest common multiple of 446116 and 44.
446116
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380653
What is the smallest common multiple of 2073 and 17275?
51825
What is the smallest common multiple of 4334 and 59494?
654434
What is the common denominator of -47/6352 and -65/11116?
44464
What is the smallest common multiple of 1413 and 21663?
3401091
What is the lowest common multiple of 9290 and 26012?
130060
Calculate the smallest common multiple of 2682 and 120.
53640
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1028508
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144018
Find the common denominator of 21/19720 and -63/24650.
98600
Calculate the smallest common multiple of 22428 and 10.
112140
What is the lowest common multiple of 7238 and 1386?
65142
What is the common denominator of -155/14478 and 18/2413?
14478
Find t