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]


ppose 65*l - 5*i = 64*l - 11, 0 = -3*l - 5*i + 7. Let c(f) = -6*f**2 + f + 1. Let b be c(-2). What is the common denominator of (685/b - 1)/(l + -3) and 85/8?
40
Suppose -4 = -k + 3*w + 26, 3*k = -5*w + 160. Let m = -17911 - -17961. What is the smallest common multiple of k and m?
450
Let l = -16/103 - 3461/927. Let q = -297457/7906 - -2178/59. Calculate the common denominator of l and q.
1206
Suppose 21*v = 17*v. Suppose v = 7*a + 46 - 403. Calculate the lowest common multiple of 3 and a.
51
Let l = 21726110/11 + -1976445. Let o = l - -1447995/1078. Find the common denominator of 47/140 and o.
980
Suppose 28*v - 12892 = 6260. What is the lowest common multiple of 57 and v?
684
Let j = 95 + -73. Let p(x) = -x - 1. Let l be p(3). Let s = l - -24. What is the least common multiple of j and s?
220
What is the smallest common multiple of -11*90/330*13930/(-6) and 28?
27860
Let w(c) = -34*c**2 + 12*c + 1. Let x be w(5). Let g be (0 - 4) + x/(-27). Let r = g + -467/18. What is the common denominator of 1/20 and r?
180
Let o be 3/7 + (-1740443)/714. Let j = -2443 - o. Calculate the common denominator of -27/52 and j.
156
Suppose -24*s + 7*s = -391. Suppose -5*z + 3*h + 143 = h, -z - h + s = 0. What is the least common multiple of 33 and z?
297
Let r = 78 + 31. Let g = 123 - r. Suppose 40 - 4 = 3*q. What is the lowest common multiple of g and q?
84
Let c = -3/11744 + 149769/129184. Calculate the common denominator of c and -17/180.
1980
Calculate the smallest common multiple of (1242/108)/((-1)/(-12)) and 115.
690
Suppose -4687 = -4*a - 4671. What is the least common multiple of a and 580?
580
Let v = 290 - 278. Suppose 4*y + v = 3*k, -5*k = -5*y - 2 - 23. What is the smallest common multiple of k and 138?
552
Let v(i) = 7*i**2 + 47*i + 566. Calculate the least common multiple of 5104 and v(21).
51040
Suppose 0 = 5*v - 2*t - 11370, 11*t = -4*v + 14*t + 9096. Calculate the lowest common multiple of v and 12.
4548
Let s = -35653 - -35673. What is the smallest common multiple of s and 1195?
4780
Let d = 22 - 12. Suppose -2*b - d = -7*b. Suppose 0 = 2*u + b*w - 48, 2*w + 8 = 6*w. What is the lowest common multiple of 4 and u?
44
Suppose 140 = 10*p - 3*p. Suppose -26*z + p = -22*z, -2*v - 3*z = -75. What is the lowest common multiple of v and 45?
90
Let w = -63561/230 - -4133/15. Calculate the common denominator of 79/10 and w.
690
Suppose -r + 1 = g, -2 = 3*g - 4*r + 2. Suppose g = -20*c + 9*c + 462. What is the lowest common multiple of c and 3?
42
Suppose 4*j + 1520 = 3*q - 614, -5*q = -2*j - 3566. Find the common denominator of q/(-1176) + 0 + 8/2 and -25/7.
28
Calculate the common denominator of -14*17/60*11*30/220 and (-6)/(-28)*(-1)/3.
140
Calculate the common denominator of -43/210 and 708/(-252)*-4 - 12.
210
Let c = 2/2217 + -3707/13302. Let k = 51829 + -2487673/48. Calculate the common denominator of k and c.
144
Let c = -206875/13 + 31851/2. Let t = c + -31481/2574. Calculate the common denominator of t and -73/44.
396
Find the common denominator of (-517)/(-528) - 6/8 and -79/460.
5520
Let n = -17409388/16989 - -3877/809. Let l = n - -3064/3. What is the common denominator of -99/14 and l?
42
What is the common denominator of 19/120 and (((-84)/(-240))/7)/(16/(-452))?
240
Let b = -155239/17 + 9129. Let r(a) = -a**2 + 2*a + 4. Let s be r(4). Find the common denominator of b and s + (-212)/(-40) + -3.
170
What is the common denominator of 4 + 1 + 6/(-3696)*3070 and 31/110?
1540
Let w = -32555/10906 + 44/779. Let j(z) = -z**2 - 3*z - 1. Let m be j(-2). Calculate the common denominator of 101/(-12) - m*-1 and w.
84
Suppose 151*y - 155*y + 344 = 3*l, 0 = 5*l + 4*y - 568. Calculate the smallest common multiple of l and 42.
336
Calculate the common denominator of 79/4 and (11 - (-1236)/(-48))/(8120/32).
4060
Suppose -4*k = -7*k - 108. Let i be (2 - 4) + k/(-2). Find the common denominator of 39/10 and (900/(-486))/(i/(-6) - 0).
180
Let z(s) = 12*s**2 - 5*s - 4. Let k be z(-1). Calculate the common denominator of 71/4 and 83/12 - (7 - k/2).
12
Suppose 3*z = o - 505, -3*z + z + 4*o - 320 = 0. Let q = 179 + z. What is the least common multiple of 30 and q?
90
Suppose 2*r + 4*f = 4508, 2*r - 5*f = 4*r - 4505. What is the smallest common multiple of r and 16?
9040
Suppose -457 = 28*b + 271. Let k(x) = -2*x**2 - 46*x + 168. Suppose 4*s - 27 = -3*h + s, 4*s = 2*h. What is the lowest common multiple of k(b) and h?
12
Let i = 37010773/44 - 841153. Let d = -7198 - -71871/10. Calculate the common denominator of d and i.
220
Let q(h) = h**3 + 3*h**2 - 6*h. Let k(m) = m**3 - m - 1. Let o(i) = 2*k(i) - q(i). Let v be o(2). What is the least common multiple of 26 and v/10 + 4 + 474/30?
260
Let o = -4889183/474903030 + -4/212961. What is the common denominator of o and 44/1115?
2230
Suppose -5*p - 2*f + 1506 = -0*f, 5*f = 3*p - 885. Let c = 2/193 - -2891/386. What is the common denominator of c and 4/(-6) + (-1465)/p?
20
Suppose -9*g + 13*g = 132. Suppose -2*h = 5*l - g, 7*l = 5*l - 4*h + 26. Calculate the smallest common multiple of 41 and l.
205
Let h(i) = -1040*i**2 + 82*i + 237. Let f be h(-3). Let j be 33739/(18/5*1). Let u = j + f. What is the common denominator of -53/20 and u?
180
Suppose 0 = -s - 3*s + 48. Suppose -15*a = -s*a - 171. Suppose 0 = -8*j + 15 + a. Calculate the lowest common multiple of 7 and j.
63
Suppose 12*o - 28*o + 26180 = 18*o. What is the lowest common multiple of o and 550?
3850
Suppose -141*q + 126880 = -19*q. What is the least common multiple of q and 585?
9360
Let s = 73660 + -5156343/70. Find the common denominator of 155/714 and s.
3570
Let h(l) = -84*l**2 + 4*l - 7. Let w be h(1). Suppose -2*p + t = -221 + 14, p - 3*t - 116 = 0. Let b = w + p. What is the smallest common multiple of b and 22?
154
Let j(h) = 144*h + 1652. Calculate the lowest common multiple of j(-8) and 350.
3500
Find the common denominator of -83/128 and 156599/201792 + ((-4)/(-6) - 2/2).
384
What is the common denominator of -57/22 and (24/(-32)*-92*(-3)/72)/17?
1496
Let q = 1031/47 + -8627267/393296. Let s = q + 240553/75312. Calculate the common denominator of s and (-84)/(-88) - (4 - 0).
396
Suppose 0 = -4*j + 11*l - 8*l + 74, 0 = -5*j - 3*l + 106. Calculate the lowest common multiple of 18 and j.
180
Let y = -5149/102858 + -28/237. Find the common denominator of -95/124 and y.
868
Let t(s) = -4*s + 27. Let q be t(5). Find the common denominator of (56/128)/q*2 and 143/18.
72
What is the common denominator of 49 - 38 - 4934/438 and 23/657?
657
Let x = -7376450/189 + 39029. What is the common denominator of -17/1782 and x?
12474
Find the common denominator of 125/234 and (-42)/693*(79/(-4))/(-1 - 0).
2574
What is the least common multiple of (1 - 2) + 162 + -25 + 20 and 92?
3588
Let p(j) = -21 - 22*j - 15*j - 30 + 22*j. What is the smallest common multiple of p(-5) and 40?
120
Suppose 0 = 32*u - 55*u + 2361 + 1779. What is the least common multiple of 60 and u?
180
What is the lowest common multiple of 32/(4 - (3 + -1)) and 898?
7184
Suppose 0 = 8*o - 7*o - 620. Suppose o - 44 = 9*a. Find the common denominator of (-3)/3 - ((-444)/a - -1) and -15/44.
176
Suppose -7*d - 10*d + 17 = 0. Let t(k) = -2*k**3 - k + 2. Let p be t(d). What is the common denominator of -121/6 and (-5)/(-70)*(71/12)/p?
168
Let m be 5 + (2 - (-377394)/360). Let h = m + -6341/6. What is the common denominator of 76/15 and h?
60
Let j(a) = -2*a**3 - 21*a**2 + 13*a + 17. Suppose 56 - 111 = 5*c. Let d be j(c). Find the common denominator of 47/24 and d/15 - (-46)/14.
168
Suppose 10*c - 11*c - 4 = 0. Let t be -329083*5/(-5700) - (-1)/c. Let s = -5530/19 + t. Find the common denominator of 73/33 and s.
330
Let j = -427439/28 + 15262. Let x be (-3)/6*(-12)/(-383). Let r = x - -7313/2298. Calculate the common denominator of r and j.
84
Suppose -6*a - 538 = -7*a + 5*c, -3*c + 2152 = 4*a. Let w = a + -4846/9. What is the common denominator of w and 107/216?
216
Let q = 57 + -41. Suppose -q = -4*x, -12*s - 24 = -13*s - 2*x. What is the lowest common multiple of s and 44?
176
What is the common denominator of 15862/52808 + -4*1*1/46 and -23/82?
164
What is the common denominator of (28/168)/((-1442)/60627) + 7 and (-4)/18 + (-566)/72?
1236
Let w(z) = -4345*z - 52. Let y be w(14). Let a = -5844617