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
Generally, the invention relates to detecting data inversions between electronic devices in communication with one another. More specifically, the invention relates to detecting a data inversion based on the determination of a received invalid sequence of data and automatically correcting the data inversion by logically changing the polarity of the received data.
2. Discussion of the Related Art
Differential Signaling, such as Low voltage differential signaling (LVDS), is generally a type of serial data communications where a voltage difference between two wires is used to convey information. In LVDS, a transmitter simultaneously applies a voltage to a wire and the inverse of the voltage to a paired wire. When summed together, the voltage equals zero and any electromagnetic radiation (EMR) generated by one wire is canceled out by the other. A receiver subtracts the voltage on the two wires to recover the signal sent by the transmitter. Subtracting the signals on the two wires generally allows the same signal to be transmitted with half the voltage on each wire, thereby using less power. LVDS also improves signal to noise ratio (SNR) because any noise added to the wires is roughly uniform between the wires and removed by the receiver. Decreased transmit power, decreased EMR, and increased SNR make LVDS very useful in high speed data communications.
Accordingly, LVDS is often employed in computer devices requiring relatively fast data transfer rates, such as computer disk drives. The high speed of LVDS and its use of in-channel synchronization generally allows more data to be sent using fewer wires than can be done with a normal parallel bus. Some examples of LVDS used in computer communications include HyperTransport, SCSI, RS-422, RS-485, Ethernet, Universal Serial Bus (USB), Serial Advanced Technology Attachment (SATA), Serial Attached Small Computer System Interface (SAS), and FireWire.
Many computer devices further enhance the reliability of the transmitted data by formatting the data with a communications protocol. A communications protocol is a set of standard rules for data representation, signaling, authentication, and error detection and correction used in transmitting information. One example of such a protocol includes the PCI express (PCIe) protocol. PCIe is a “point-to-point” bus protocol that removes the need for arbitrating with a computer bus such that a transmitter need not wait until the bus is free to transmit data. One feature of PCIe is its ability to negotiate communications between the transmitter and receiver. For example, when a transmitting computer device (e.g., a host processor on a motherboard) wishes to transmit data to a receiving computer device (e.g., a PCIe card coupled to the motherboard), the transmitting computer device may negotiate communications through a “handshaking” sequence that the receiving computer device acknowledges. In this regard, the transmitting computer device may transfer a sequence of data that is used by the receiving computer device to determine the polarity of the data being transmitted. If the receiving computer device determines that the polarity of the data is inverted, the receiving computer device may inform the transmitting computer device of the data inversion such that one of the computer devices reverses polarity.
While this polarity negotiation between computer devices ensures that the devices will be communicating in the correct polarity, it generally requires implementation within both transmitting computer devices and receiving computer devices. However, some communication protocols are not configured with such a polarity negotiation. Accordingly, devices operating with these polarity correction lacking protocols require design assurance that the devices are properly connected. For example, the SAS protocol does not include a specific polarity checking sequence in which a receiving device may determine a polarity inversion and notify the transmitting device of that inversion. Accordingly, designers must assure that a SAS interface to a SAS device, such as a computer disk drive, has its serial data connections coupled to the device in the correct polarity during assembly. Otherwise, literally half of the SAS devices may require reconfiguration after assembly.
It is evident from the above discussions that there is a need for automatically correcting data inversions for computer devices using communication protocols that lack specific polarity checking sequences.