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]


68414820 + 4329/120397. Let x = y - -89/85. What is the common denominator of -67/18 and x?
36
Let q = -2540441/90 + 28228. Find the common denominator of 79/1053 and q.
10530
Suppose 2*g - 11890 = -3*g. Let v = 6841187 + -123184189/18. Let w = g + v. Calculate the common denominator of -19/7 and w.
126
Let y(d) = -d + 33. Let c be y(-9). Suppose 5*t + 2*n = 589, 4*n = -2*t + c + 200. Let q = 119 - t. What is the smallest common multiple of 18 and q?
18
Let k = 179 - -10056. Let n = k - 921187/90. Calculate the common denominator of 7/90 and n.
90
Suppose 0 = 17*f + 55 - 21. Let s(j) = -2*j**2 - 15*j - 10. Calculate the smallest common multiple of 48 and s(f).
48
Calculate the common denominator of 91/10 and 76/190 - (4 + ((-7846)/2460 - 0)).
1230
Let f be (11/(-132))/((-477)/192). Let s = 2390/1431 + f. Find the common denominator of s and -74/33.
297
Let q = 4966 + -4234. Calculate the least common multiple of 32 and q.
5856
Let u = 1747 - 1743. Calculate the smallest common multiple of 30 and u.
60
Let b = -168 + 186. Suppose 0*d - 160 = -4*d. Suppose -16*x = -b*x + d. What is the smallest common multiple of x and 50?
100
Suppose -9*z + h - 2772 = -11*z, 5544 = 4*z + h. Calculate the lowest common multiple of z and 198.
1386
Let o be 3066/15 + (-72)/(-45). Let i = -831/4 + o. What is the common denominator of (-4)/18 + (-145)/(-126) and i?
28
Let i(s) = 45*s - 43. Let j be i(1). Suppose -4*b - b = -15. Suppose -6*k - t = -2*k - 52, b*t = j*k - 12. What is the lowest common multiple of 6 and k?
12
Let r = -98555/792 - -1370/11. Find the common denominator of r and -29/72.
792
Suppose 0 = 5*f - 15*f - 630. Calculate the common denominator of (-1 + (-4)/(-19))/8 and ((-7)/6)/(f/(-7) - 6).
1368
Let s = -304964546/12045 - -126594/5. Find the common denominator of s and 133/438.
4818
Let y = -588635 + 197781509/336. What is the common denominator of 199/210 and y?
1680
Let r = -3915560/300631321 + 6/114701. Calculate the common denominator of -99/8 and r.
20968
Let i = -280152/2486171 + 186/2999. Calculate the common denominator of 63/5 and i.
4145
Let o = -18474 + 665131/36. Let p = -1235803/30 - -82375/2. Calculate the common denominator of o and p.
180
Find the common denominator of -70/3 and (-283578)/(-17712) + -9 + -7.
2952
Let h = 737/161 - 1528/23. Let r = h - -4289/63. Calculate the common denominator of r and (62/7)/(6/(-14)).
9
What is the common denominator of -2/5 and (1 - 4787/4688)/(546/28 - 22)?
11720
Let l = -52 - -50. Let y = 68 - 22. What is the common denominator of (l/40)/(-2*(-12)/(-2464)) and y?
15
Let f = -12467 - -37367/3. Calculate the common denominator of f and 58/1749.
1749
Let i = 167 - 663/4. Let l = 43231/30 + 247/15. Let t = -1423 + l. Find the common denominator of t and i.
4
What is the smallest common multiple of 1267 and (-16)/1 - (-242223)/263?
6335
Let o = -1638349/79128 + 3213/157. What is the common denominator of -139/24 and o?
504
Let l = 1263771/1168090 - 1/10619. Find the common denominator of -41/70 and l.
770
Calculate the lowest common multiple of 26 + 6*(-2)/3 and 1 + -2 + 1 + -171 + 173.
22
Let l be 3/((18/(-27))/(8/18)). Let p = 62 + l. What is the smallest common multiple of p and 132?
660
Let z = 625 - 437. Calculate the common denominator of 1 - ((-472)/z + 3) and -21/8.
376
Let p(r) = 2*r**3 - 76*r**2 + 41*r - 242. Calculate the smallest common multiple of 752 and p(38).
5264
Find the common denominator of (8/8448*268)/(3/(54/24)) and 69/440.
1760
Let s = 53 + -54. Let q be ((-3)/6)/(s/(-4)). Find the common denominator of ((-35)/40)/(1/13*q) and 59/4.
16
Let x be 1/(3 + 2136/(-714)). Calculate the common denominator of (31/(-7))/(340/x) and (-1 - -2) + (-142)/12.
60
Let t be (6271/16 - -1)*420/(-315). Let w = -522 - t. Calculate the common denominator of -77/20 and w.
60
What is the common denominator of (-2 - (-417)/210)*4526/657 and -71/1260?
1260
Let t = -11397773326/8715 + 1307834. Calculate the common denominator of 28/33 and t.
95865
Let g = 10892 + -10806. What is the smallest common multiple of 8 and g?
344
Let d be 8/(-20)*(14 + 1). Suppose 0 = -i - 3*x - 15, 4*i - 4*x + 41 + 35 = 0. Find the common denominator of (d - 171/(-30))/(i/445) and -77/36.
36
Let c = -6495 - -6756. What is the smallest common multiple of c and 87?
261
Let q = -13/392 - 2369/1176. Let u = -20687/2481 - -4/827. Calculate the common denominator of q and u.
21
Let c = -2038 + 2050. Calculate the lowest common multiple of 140 and c.
420
Let p = -595526/1024905 + 1/9761. Calculate the common denominator of p and -6/343.
5145
Calculate the common denominator of 12 + -12 + (-1 + -72)/(-1593 + 1) and -101/2388.
4776
Let m(r) = 2*r**2 + 44*r + 256. Calculate the least common multiple of (1 - (-3184)/4) + 1 and m(-10).
6384
Let h = -17 - -27. Calculate the common denominator of (822/15)/(132/55) and 35/2*(-2)/h.
6
Let z = -660 + 658. Suppose -3*m + 2*d - 255 = 810, -3*m = 4*d + 1065. What is the common denominator of ((m/7)/(-5))/(z + 4) and 109/14?
14
Find the common denominator of (-10 - -6) + ((-26)/(-65) - 8983/(-2530)) and -127/230.
2530
Calculate the common denominator of (-1598)/6384 - (18 - 219/12) and 69/2.
3192
Suppose 360 - 8 = 5*j - f, -8*j + 3*f + 552 = 0. What is the least common multiple of j and 24?
72
Suppose -32 = -76*n + 1032. What is the lowest common multiple of n and 12824?
12824
Let u(k) = -k**3 - 29*k**2 - 9*k + 53. Let c be u(-20). Let x = -26883/8 - c. What is the common denominator of x and -79/172?
344
Let d(c) = -c**2 + 36*c + 117. What is the smallest common multiple of d(34) and 1?
185
Let l = 156 + -135. Suppose 14*b = l*b - 168. What is the lowest common multiple of 76 and b?
456
Let w(u) = -u**3 + 27*u**2 - 6*u + 228. Calculate the smallest common multiple of w(27) and 1892.
5676
Suppose 5 = -5*b, 0 = 3*z + 4*b + 427274 - 124351. Let t = z - -13126411/130. Find the common denominator of t and -19/4.
260
Let t(y) = -87*y + 5. Let h be t(3). Let m = h + 175. Let u = m + 83. Calculate the smallest common multiple of u and 8.
8
Suppose -106*l + 1332*l = 9808. Let r(k) = -2 + 0*k**2 + 2*k - 2*k**2 + 3*k**2. What is the lowest common multiple of r(-4) and l?
24
Suppose -1207 = -6*x - 439. Suppose -x*b + 350 = -123*b. Calculate the smallest common multiple of b and 50.
350
Let n be (1065/(-6))/(57/190). Let y = -2353/4 - n. Calculate the common denominator of -38/9 and y.
36
Suppose -t - 4 = y, -2*y + 0*y + 2*t - 20 = 0. Let p be (-25)/3 + (-54)/81. Let j = y - p. What is the lowest common multiple of j and 6?
6
Let k = -3 + 13. Let a = -3583 - -3653. What is the lowest common multiple of k and a?
70
What is the lowest common multiple of (6923 + 7)/11 + -2 and 6?
1884
Calculate the common denominator of 7/189*-1*(-867)/34 and 8/2037.
12222
Let x = -1868/53 - -850457/24062. Find the common denominator of x and 1/22.
4994
Let d(a) = 22*a. Let u = 133697 - 133657. Calculate the least common multiple of u and d(2).
440
Let v be (1/(-1474))/(24/(-132252)). Let h = -3/268 + v. Find the common denominator of (-413)/(-40) - 11/55 and h.
88
Let a(x) = -50*x + 870. Calculate the least common multiple of a(17) and 10.
20
Suppose -72 = -0*l - 3*l. Let c(y) = 10*y**2 + 177*y - 181. Calculate the least common multiple of c(-20) and l.
2232
Suppose 2*g + 183 - 191 = 0. Suppose -4*a + i + 354 = 0, 96 = g*a + i - 254. Calculate the least common multiple of 48 and a.
528
Find the common denominator of 21/260 and ((-354)/60 - -1)*((-72)/78 + 1).
260
Let z = -483/2 + 246. Suppose 0 = -4*t + v, 5*t = v + 2 - 1. Calculate the common denominator of z and t/4 - (-3850)/968.
22
Suppose -h - s - 50 = -2*s, 0 = 4*h + 4*s + 168. Let t = -38 - h. What is the lowest common multiple of 14/1 + (6 - 8) and t?
24
Let m(j) = -j**3 - 159*j**2 + 484*j - 315. Let s = -630 + 1001. Calculate the least common multiple of s and m(-162).
3339
Let k = -12 + 19. What is the smallest common multiple of (-6)/(3*k/(-84)) and 2/(-5) - 96/(-15)?
24
Let k = -193693886827 + 53127715136257397/274287. Let r = -242/507 + k. Let v = -27809/25968 - r. What is the common denominator of v and -11/8?
48
Let g(r) be the first derivative of -19*r**2/2 - 258*r + 15. What is the least common multiple of 344 and g(-14)?
344
Let s = -14 + 56. Let t b