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]


(a) Field of the Invention
The present invention relates to a large-aperture macro lens system and, more particularly, to a large-aperture macro lens system which is capable of photographing an object at the infinite distance up to an object at a distance corresponding to the photographing magnification of 1.times. and which has a focal length of 50 mm and large aperture ratio, i.e., F/2.8.
(b) Description of the Priot Art
For photographic lens systems in general, aberrations are corrected so that the lens system displays the best performance when it is focused on an object at the infinite distance. On the other hand, for macro lens systems, a photographing magnification about 1/10.times. is used as the standard photographing magnification, and aberrations are corrected so that the performance of the lens system becomes favourable when it is focused on an object at a distance corresponding to the standard photographing magnification.
However, in case of such macro lens systems, it is impossible to satisfactorily correct the variation of aberrations which occur according to the variation of the photographing magnification and, when the lens system is focused on an object at a distance shorter than the object distance corresponding to the standard photographing magnification, the lens system causes spherical aberration, coma, etc. largely. Especially, in case of a lens system such as, for example, Gauss type lens system which is arranged to be symmetrical in respect to the stop, there is general tendency that, as the photographing magnification is made higher, spherical aberration to be caused by rays of intermediate heights is undercorrected and spherical aberration to be caused by rays of the maximum height is overcorrected. As a result, the quality of image decreases considerably, and it is impossible to effectively utilize the strong point of a large aperture macro lens system. This is because paraxial rays, which go out from the lens components arranged in front of the stop and which are converging rays in respect to an object at the infinite distance, gradually come to a state close to the afocal state according to the variation of the photographing magnification and, at a photographing magnification about 1.times., said paraxial rays become diverging rays. When this is examined from the view point of coefficients of aberrations, spherical aberration of the third order is undercorrected while spherical aberration of the fifth and seventh orders is considerably overcorrected. As a result, flare is caused and the quality of image decreases.
The above-mentioned problem is evident from the coefficients of spherical aberration of Embodiment 1 of a known macro lens system, which is disclosed in Japanese published examined patent application No. 20006/83, when the lens system as a whole is advanced. Said coefficients of aberration are as shown below.
______________________________________ SA3 SA5 SA7 Total ______________________________________ Infinite Distance -0.109 +0.076 +0.027 -0.006 -0.5X -0.246 +0.241 +0.089 +0.084 -1.0X -0.201 +0.427 +0.171 +0.397 ______________________________________
In the table shown in the above, values of respective coefficients of aberration correspond to values of lateral aberration on the image surface to be caused by paraxial rays of the maximum height. Here, reference symbol SA3 represents the coefficient of spherical aberration of the third order, reference symbol SA5 represents the coefficient of spherical aberration of the fifth order, and reference symbol SA7 represents the coefficient of spherical aberration of the seventh order.
The floating method is known as a means for correcting the variation of aberrations which occurs at the time of focusing on an object at a short distance as described in the above. Macro lens systems to which the floating method is applied are disclosed in Japanese published unexamined patent applications Nos. 28038/80, 107208/81, etc. Each of the above-mentioned known macro lens systems comprises two lens groups, i.e., a front lens group (a first lens group) located in front of a stop, and a rear lens group (a second lens group) located in rear of the stop. Another known macro lens system, which is disclosed in Japanese published unexamined patent application No. 192916/82, is arranged to comprise a front lens group (a first lens group) located in front of a stop, a rear lens group (a second lens group) located in rear of the stop, and a third lens group having positive refractive power which is added on the image side of said rear lens group, and still another known macro lens system, which is disclosed in Japanese published unexamined patent application No. 228220/84, is arranged to comprise a front lens group (a first lens group) located in front of a stop, a rear lens group (a second lens group) located in rear of the stop, and a third lens group having negative refractive power which is added on the image side of said rear lens group. Each of the known macro lens systems described so far is arranged that floating is carried out, when focusing on an object at a short distance, by varying an airspace between respective lens groups in the monotone increasing pattern.
The known macro lens systems described so far are respectively arranged that, when focusing on an object at the shortest object distance from the state that the lens system is focused on an object at the infinite distance, an airspace between respective lens groups is varied in the monotone increasing pattern so as to increase the heights of paraxial rays on a converging surface contained in the second lens group and to thereby cause undercorrected spherical aberration so that overcorrected spherical aberration to be caused by rays of the maximum height is offset by said undercorrected spherical aberration, and the variation of spherical aberration to be caused when focusing on an object at a short distance is thereby corrected. However, the above-mentioned method has disadvantages described below. That is, up to a photographing magnification about 1/2.times., it is possible to correct spherical aberration favourably. However, at a photographing magnification about 1.times., undercorrected spherical aberration occurs largely, flare is caused in the central portion of the image surface and, as a result, the quality of image becomes unfavourable. Moreover, the displacement of the image surface to be caused when the stop is stopped down becomes large. Furthermore, the advancing amount of the lens system at the time of focusing becomes large, and it is impossible to make the lens system compact.
Still another known macro lens system is disclosed in Japanese published unexamined patent application No. 100115/85. Said known macro lens system comprises a first lens group having positive refractive power, a second lens group having positive or negative refractive power, and a third lens group having positive refractive power and is arranged to perform floating, when focusing on an object at a short distance, by varying the airspace between the first and second lens groups in the monotone increasing pattern and varying the airspace between the second and third lens groups in such pattern that said airspace increases and, then, decreases.
Generally, when a macro lens system is focused on an object at a distance corresponding to the photographing magnification about 1.times., the lens system advancing amount required becomes equal to the focal length of the lens system in the state that the lens system is focused on an object at the infinite distance. Therefore, even when the lens system is arranged compactly, the product provided with a lens system advancing mechanism does not become compact in most cases. In case of the above-mentioned known macro lens system disclosed in Japanese published unexamined patent application No. 100115/85, both of the first and second lens groups have positive refractive powers. Therefore, the photographing magnification available cannot be made higher than 1/2.times., the lens system advancing amount for focusing is large, and it is impossible to obtain a compact lens system.