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]


1. Field of the Invention
The present invention relates generally to an imaging apparatus that includes two imaging optical systems that change image focusing locations, respectively, and two imagers that convert subject images formed by the two imaging optical systems into image signals, respectively.
2. Description of the Related Art
Methods of Automatic Focusing (AF) in a digital camera including imagers, such as a Charge Coupled Device (CCD) and a Complementary metal-oxide-semiconductor (CMOS), include a method called contrast AF, which scans and moves an image focusing location of an imaging optical system, acquires a contrast evaluation value in each image focusing location, detects an image focusing location having a contrast evaluation value, which is an extremum, and determines the detected image focusing location as a focus location.
FIGS. 12A to 12E illustrate an operation of a conventional imaging optical system for detecting a focus location by contrast AF.
Referring to FIGS. 12A to 12E, in the graphs, the dotted curve corresponds to a contrast evaluation value that is not yet determined yet, and the solid line corresponds to a part having already acquired a determined contrast evaluation value. When the image focusing location stays at an initial focus location, as illustrated in FIG. 12A, it is not clear which side, between the infinity (INF) side and the NEAR side, the renewed focus location is nearer to from the current image focusing location. Accordingly, the image focusing location is first scanned and moved in some degree in toward the INF or NEAR side to determine whether the contrast evaluation value increases or decreases. Thereafter, it is estimated that the focus location is nearer to the side corresponding to the increasing direction, before starting the operation.
In this operation, because it is initially unclear which side the renewed focus location is nearer to from the current image focusing location, i.e., either the INF side or the NEAR side, the current image focusing location may be moved toward a side opposite to the extremum as illustrated in FIG. 12B.
Then, as illustrated in FIG. 12C, it is required to unnecessarily perform an extra movement of the image focusing location by the distance required in order to return the image focusing location to the original position.
Thereafter, the image focusing location is continuously changed until the contrast evaluation value changes from the increasing trend to the decreasing trend as illustrated in FIG. 12D, and the renewed focus location is then determined by returning an over-moved image focusing location to the renewed focus location as illustrated in FIG. 12E, thereby completing the contrast AF.
In the contrast AF as described above, in an initial stage, a user cannot know which side the renewed focus location is nearer to from the current image focusing location. Therefore, especially as illustrated in FIG. 12B, the image focusing location may be moved away from the renewed focus location. In this case, the time necessary for the automatic focusing may be prolonged or it may be difficult to perform a smooth operation.
One method for solving the above-described problems is a called “wobbling”. In wobbling, a direction toward the focus location is detected based on the trend of increasing or decreasing a contrast evaluation value acquired by minutely moving the focus lens back and forth, as illustrated in FIG. 13.
In wobbling, there is no possibility to fail in detecting the operation direction when the image focusing location is changed toward a renewed focus location. However, because the focus lens is always driven, this method requires high power consumption, which reduces battery duration.
In a stereoscopic camera having two imaging optical systems for imaging a stereoscopic image, estimation for a direction of a focus location is not especially performed. Instead, the scanning range for contrast AF is distributed to the two focus lenses of the two imaging optical systems, in order to reduce the time for the AF to a shortest time, e.g., up to nearly one-half of the original time.
For example, a double lens camera as described in Japanese Patent Unexamined Publication No. 2006-162990 includes a first imaging optical system and a second imaging optical system, and may separately control locations of respective lenses 13. Further, if the user partially pushes a shutter button, e.g., to a degree of one-half, to start an AF operation, a focus lens 13 of the first imaging optical system is moved toward the INF end, a focus lens 13 of the second imaging optical system is moved toward the NEAR end, and respective focus lenses 13 are scan-moved to a center side as illustrated in FIG. 14, in order to find an image focusing location having a peak contrast evaluation value.
Further, in another example described in Japanese Patent Unexamined Publication No. 2006-162990, as illustrated in FIG. 15, if the user partially pushes a shutter button, e.g., to a degree of one-half, to start an AF operation, the focus lens 13 of the first imaging optical system is substantially arranged at a center of a drivable range, a focus lens 13 of the second imaging optical system is arranged at the NEAR end, and respective focus lenses 13 are then scan-moved to the INF end while maintaining a spacing distance between them, in order to detect a focus location in an imaging optical system.
As noted from the foregoing examples, in a double lens camera, the distribution of the scan-movement range to the two lenses helps reduce the time for the AF, up to nearly one-half of the original time.
However, in the contrast AF method described in Japanese Patent Unexamined Publication No. 2006-162990, in order to distribute the scanning range and to eliminate the necessity for consideration of the driving direction, the focus lens still needs to be moved first to predetermined positions, including the INF side, the NEAR side, and the center, such that a driving time is still incurred for this portion of the operation. That is, because to the conventional methods cannot start the focusing operation at the current image focusing location, the time or power consumption required for an initial arrangement increases.
Further, according to the renewed focus location or the image focusing location before the focusing operation, the initial arrangement operation may require an operation of returning the image focusing location having passed a renewed focus location to the renewed focus location, which may also cause an unnecessary movement, e.g., as illustrated in FIG. 12B.