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.

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### *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]


The present invention relates to a ball screw which converts rotation into linear motion and, more particularly, to improvements in a ball screw used for heavy-load applications.
According to a conventional ball screw, the initial contact angle and the maximum contact angle of ball-screw threads to be formed on a screw shaft or a ball nut are respectively set to about 45 degree and about 65 degree in consideration of balanced workability, operability, and load-carrying capacity.
For example, in the case of a tube-circulated type ball screw as shown in FIG. 1, if a ball screw has ball circulation paths for a plurality of circuits, the attachment positions for the circulation tube 50 of each circulation paths are concentrated into one plane in order to reduce the number of machining processes. More specifically, a plurality of circulation tubes 50a, 50b, and 50c are usually designed so as to be axially arranged into a line and also arranged in the same phase with each other in the circumferential direction as shown in FIG. 1. Note that FIG. 1 shows the ball screw having three circulation circuits.
In a case where a ball screw is designed, a slightly large safety factor is set, so that a ball screw having a sufficient shaft diameter to satisfy working conditions is usually selected. At this time, if the shaft diameter of the ball screw cannot be increased, usually the number of circuits formed in a ball nut 51 or the number of balls is increased, or the lead of the thread of the ball screw is increased to thereby increase the diameter of a ball.
In the meanwhile, in the prior art, the selection of a suitable ball screw is made in consideration of load conditions on the basis of an assumption that load is uniformly exerted on all-balls rotating in the space between a screw shaft 52 and the ball nut 51. Namely, in the prior art, the suitable ball screw is selected by calculating a contact pressure on the basis of an averaged load which is obtained by dividing the load by the number of effective balls constrained to the ball nut 51, and comparing the thus-calculated contact pressure with a database concerning the function and life of the ball screw obtained as a result of tests.
In practice, however, the load is not uniformly exerted on all the so-called effective balls rotating in the space between the screw shaft 52 and the ball nut 51. Axial dispersion arise in the distribution of loads on the inside of the ball nut 51 owing to the elastic deformation of the screw shaft 52 and the ball nut 51 caused when they are subjected to the load. For example, similar to a case where heavy-weight material is machined on a work table supported by a ball screw, in a case where axial load Fa is exerted on the ball nut 51 of the ball screw and another axial load Fa' is exerted on the screw shaft 52 in the directions as shown in FIG. 2, the axial distribution of elastic displacements of the ball nut 51 and the screw shaft 52 in respective ball-screw threads 51a, 52a are represented by arrows shown in FIG. 2. It is understood that stress concentrates on the points of contact between the balls and the opposite ends of the ball nut 51 in accordance with the amount of elastic displacement of the screw shaft 52 and the ball nut 51.
The balls rotating in the respective circulation paths are sequentially scooped on and fed to a circulation tube 50 from the ball-screw threads 51a, 51b and are circulated. The balls are in contact with only the threads of the screw shaft 52 which are opposite to the ball nut 51. For this reason, dispersions also arise in the distribution of loads in the circumferential direction, thereby imposing heavy loads on a part of the effective balls. FIG. 3 shows the circulation of the balls of each circuit within the ball nut 51. As shown in FIG. 4, as a result of feeding the balls 1 to the circulation tube 50 from the ball-screw threads, the number of balls existing in the circumferential range of the ball nut 51 which has angle .beta. is comparatively reduced when the ball nut 51 is viewed in the direction of the axis. Eventually, the load exerted on the balls existing in the range having angle .beta. is comparatively increased.
As described above, as a result of the such concentrations of stress on the contact points between the balls and the opposite end portions of the ball nut 51 and the such increase in the load exerted on the balls which exist in the specific range of the ball circulation path, there are problems that the surface of the ball-screw threads 51a, 52a of the ball nut 51 and the screw shaft 52 is flaked at early time or abnormally abraded if the designed safety factor of the conventional ball screw is set on a small value.
For heavy load applications, if the safety factor is set to a large value, the size of the ball screw becomes large and fails to meet desired specifications or is costly.