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]


Évariste Galois, (born October 25, 1811, Bourg-la-Reine, near Paris, France—died May 31, 1832, Paris), French mathematician famous for his contributions to the part of higher algebra now known as group theory. His theory provided a solution to the long-standing question of determining when an algebraic equation can be solved by radicals (a solution containing square roots, cube roots, and so on but no trigonometry functions or other nonalgebraic functions).

Galois was the son of Nicolas-Gabriel Galois, an important citizen in the Paris suburb of Bourg-la-Reine. In 1815, during the Hundred Days regime that followed Napoleon’s escape from Elba, his father was elected mayor. Galois was educated at home until 1823, when he entered the Collège Royal de Louis-le-Grand. There his education languished at the hands of mediocre and uninspiring teachers. But his mathematical ability blossomed when he began to study the works of his countrymen Adrien-Marie Legendre on geometry and Joseph-Louis Lagrange on algebra.

Under the guidance of Louis Richard, one of his teachers at Louis-le-Grand, Galois’s further study of algebra led him to take up the question of the solution of algebraic equations. Mathematicians for a long time had used explicit formulas, involving only rational operations and extractions of roots, for the solution of equations up to degree four, but they had been defeated by equations of degree five and higher. In 1770 Lagrange took the novel but decisive step of treating the roots of an equation as objects in their own right and studying permutations (a change in an ordered arrangement) of them. In 1799 the Italian mathematician Paolo Ruffini attempted to prove the impossibility of solving the general quintic equation by radicals. Ruffini’s effort was not wholly successful, but in 1824 the Norwegian mathematician Niels Abel gave a correct proof.

Galois, stimulated by Lagrange’s ideas and initially unaware of Abel’s work, began searching for the necessary and sufficient conditions under which an algebraic equation of any degree can be solved by radicals. His method was to analyze the “admissible” permutations of the roots of the equation. His key discovery, brilliant and highly imaginative, was that solvability by radicals is possible if and only if the group of automorphisms (functions that take elements of a set to other elements of the set while preserving algebraic operations) is solvable, which means essentially that the group can be broken down into simple “prime-order” constituents that always have an easily understood structure. The term solvable is used because of this connection with solvability by radicals. Thus, Galois perceived that solving equations of the quintic and beyond required a wholly different kind of treatment than that required for quadratic, cubic, and quartic equations. Although Galois used the concept of group and other associated concepts, such as coset and subgroup, he did not actually define these concepts, and he did not construct a rigorous formal theory.

While still at Louis-le-Grand, Galois published one minor paper, but his life was soon overtaken by disappointment and tragedy. A memoir on the solvability of algebraic equations that he had submitted in 1829 to the French Academy of Sciences was lost by Augustin-Louis Cauchy. He failed in two attempts (1827 and 1829) to gain admission to the École Polytechnique, the leading school of French mathematics, his second attempt marred by a disastrous encounter with an oral examiner. Also in 1829 his father, after bitter clashes with conservative elements in his hometown, committed suicide. The same year, Galois enrolled as a student teacher in the less prestigious École Normale Supérieure and turned to political activism. Meanwhile he continued his research, and in the spring of 1830 he had three short articles published. At the same time, he rewrote the paper that had been lost and presented it again to the Academy—but for a second time the manuscript went astray. Jean-Baptiste-Joseph Fourier took it home but died a few weeks later, and the manuscript was never found.

The July Revolution of 1830 sent the last Bourbon monarch, Charles X, into exile. But republicans were deeply disappointed when yet another king, Louis-Philippe, ascended the throne—even though he was the “Citizen King” and wore the tricoloured flag of the French Revolution. When Galois wrote a vigorous article expressing pro-republican views, he was promptly expelled from the École Normale Supérieure. Subsequently, he was arrested twice for republican activities; he was acquitted the first time but spent six months in prison on the second charge. In 1831 he presented his memoir on the theory of equations for the third time to the Academy. This time it was returned but with a negative report. The judges, who included Siméon-Denis Poisson, did not understand what Galois had written and (incorrectly) believed that it contained a significant error. They had been quite unable to accept Galois’s original ideas and revolutionary mathematical methods.

The circumstances that led to Galois’s death in a duel in Paris are not altogether clear, but recent scholarship suggests that it was at his own insistence that the duel was staged and fought to look like a police ambush. In any case, anticipating his death the night before the duel, Galois hastily wrote a scientific last testament addressed to his friend Auguste Chevalier in which he summarized his work and included some new theorems and conjectures.

Galois’s manuscripts, with annotations by Joseph Liouville, were published in 1846 in the Journal de Mathématiques Pures et Appliquées. But it was not until 1870, with the publication of Camille Jordan’s Traité des Substitutions, that group theory became a fully established part of mathematics.

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(1811-32). The work of a French mathematician, the prodigy Evariste Galois, was important in the development of modern algebra. His vital contributions to group theory, a part of higher algebra, showed the impossibility of trisecting the angle and squaring the circle, and answered many other long-standing questions.

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