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]


1. Field of the Invention
The present invention relates to a sheet feeder and, more particularly, to a sheet feeder equipped with a function of detecting double feed of sheets.
2. Description of the Related Art
There has been known a conventional sheet feeder relevant to the present invention including: a sheet supplying roller for feeding a sheet from a sheet supplying portion; a registration roller arranged at a predetermined interval from the sheet supplying roller; a wave transmitter provided on the way of a sheet feed path extending from the sheet supplying roller to the registration roller, for transmitting an ultrasonic wave; and a wave receiver for receiving the ultrasonic wave transmitted from the wave transmitter; wherein the wave transmitter transmits the ultrasonic wave to a sheet in the state in which the sheet is held between both of the sheet supplying roller and the registration roller, so that it is detected, by comparing an attenuation degree of the ultrasonic wave received by the wave receiver with a predetermined threshold, as to whether or not the sheets are doubly fed (see, for example, Japanese Unexamined Patent Publication No. 2005-162426).
In recent years, high-speed printing has been progressed in an image forming apparatus such as a copying machine or a printer.
For this purpose, a sheet feeder mounted on the image forming apparatus has been required to feed a sheet such as a document or a recording medium at a high speed.
However, there has been a high possibility of double feed of sheets in superimposition when a sheet is fed from a sheet supplying portion having sheets contained therein or stacked thereon onto a sheet feed path if the sheet is to be forcibly fed at a high speed.
Double feed of the sheets in superimposition is a major cause of a paper jam.
Even if no paper jam is caused, there occurs an inconvenience that an image different from an image to be read by an image reading unit is read in the doubly fed state, or that an image to be formed on a single sheet is formed over a plurality of superimposed sheets in an image forming unit.
As a consequence, the sheets cannot be sufficiently fed at a high speed only by increasing drive speed of feeding means such as a sheet supplying roller or a feeding roller. A function of securely detecting double feed of the sheets is required in the case where the sheets are fed in superimposition onto the sheet feed path.
Examples of means for detecting double feed of the sheets generally include an ultrasonic wave sensor disposed on the sheet feed path.
Such an ultrasonic wave sensor is constituted of a wave transmitter, which transmits an ultrasonic wave, and a wave receiver, which receives the ultrasonic wave transmitted from the wave transmitter so as to convert the ultrasonic wave into electric energy.
An attenuation degree of the ultrasonic wave received by the wave receiver can be compared with a predetermined threshold by utilizing the attenuation of the ultrasonic wave transmitted from the wave transmitter when the ultrasonic wave passes through the sheet, thereby detecting as to whether or not the sheets are doubly fed.
However, since the ultrasonic wave is transmitted via air as a medium, an output from the wave receiver is fluctuated if an amplitude, that is, a fluctuation of the sheet on the sheet feed path is large, thereby making it difficult to securely detect double feed.
In the above-described prior art, the ultrasonic wave is transmitted from the wave transmitter in the state in which the sheet is held between both of the sheet supplying roller and the registration roller, thus eliminating the fluctuation of the output from the wave receiver caused by the fluctuation of the sheet.
However, the sheet feeding is once stopped by the registration roller after the sheet is fed from the sheet supplying roller, and then, the sheet is held between both of the sheet supplying roller and the registration roller. Therefore, there is a limitation from the viewpoint of the sheet feeding at a high speed.
In addition, a design is limited such that the sheet supplying roller and the registration roller must be arranged with an interval shorter than the length of a sheet having a smallest size, and further, that the ultrasonic wave sensor must be interposed between the sheet supplying roller and the registration roller.