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 invention relates to domestic appliances which commonly use at least one AC induction drive motor such as clothes washers, dishwashers, clothes dryers, trash compactors, food refrigerators, heat pumps and air conditioners. In particular the invention relates to (1) a motor phase monitoring circuit means for generating one independent motor phase sample during each line voltage half cycle and (2) appropriate appliance microcomputer program routines which use the above phase samples to infer motor output torque for the purpose of controlling operation of the appliance.
2. Description of the Prior Art
A power factor control system for AC induction motors is disclosed in U.S. Pat. No. 4,052,648 which samples line voltage and current through the motor and decreases power input to the motor in proportion to the detected phase displacement between current and voltage thereby providing less power to the motor when the motor is lightly loaded.
An electronic method and apparatus for monitoring motor torque is disclosed in U.S. Pat. No. 3,600,657 which employs a current sensitive pickup device in combination with a zero crossing detector and a pulse generator circuit for producing an analog signal which is proportional to the motor torque and which is employed to control a relay to start and stop the motor.
A circuit for monitoring the mechanical power from an induction motor and for detecting excessive heat exchanger icing is disclosed in U.S. Pat. No. 4,123,792 wherein a circuit is used in conjunction with a small resistor wired in series with the outdoor evaporator fan motor of a heat pump to develop a signal corresponding to Icos.theta. which is substantially proportional to the mechanical output of the motor. The signal is averaged for a period of several seconds by an RC integrating circuit and the averaged signal is compared to a reference load set point which must be individually adjusted for each fan motor during installation of each heat exchanger.
The present electromechanical pressure switches used for clothes washer water-level control permit user selection and control of the water fill by adjusting a control knob or lever switch which is connected by mechanical linkage to an eccentric cam which prebiases the diaphragm of the pressure switch mechanism. The present system affords the possibility of considerable operator error either by wasting hot water or by allowing all drive train components to be damaged by torque overloads due to insufficient water in the wash bath. Abrasion damage to clothes items can also result from insufficient water in the wash bath. Control systems which eliminate this problem by not allowing direct user selection or control of the water level and by instead controlling the water fill in response to some machine condition are called automatic water level controls.
Prior art clothes washer automatic water level controls are disclosed in U.S. Pat. Nos. 3,030,790; 3,359,766; 3,478,373; 3,497,884 and 3,508,287, these controls respond respectively, to torque transmitted through the wash bath from the agitator to the spin basket, wash load torque manifested as fluid pressure in a hydrostatic transmission, water flow due to clothes rollover in the wash bath, restraining torque exerted on the agitator and motion of the spin basket relative to the tub due to agitator action.
An electronic liquid level monitoring system which provides a quantitative analog-type measurement of water level in a digital format is disclosed in U.S. Pat. No. 4,201,240. A mechanical device oscillates within a coil to provide signals which are counted and a calculated multiple of the count is compared with an electronically stored table corresponding to predetermined liquid levels and the results of the comparison is utilized to initiate control functions for operating the washing machine by means of a microcomputer.
Prior art dishwasher water fill volume has generally been controlled by electrical actuation of the solenoid of a fill valve for a fixed time period, typically 120 seconds, and metering the water inlet flow rate with a flow washer having one or more orifices that are size responsive to the installation water pressure. Overflow failures are prevented by a separate float switch wired in series with the fill valve solenoid. A preset factory calibrated dishwasher fill volume must assume simultaneous worst case conditions of fast pump, full dish loading, high sudsing detergent and high line voltage to guarantee that all units will always operate with sufficient water to avoid pump starvation. This often results in some wasted hot water when any or all of the above worst case conditions are not present. Dishwasher controls which automatically terminate the water fill as soon as sufficient water is present in the dishwashing system to allow smooth water pumping at a maximum flow rate with no water starvation under a wide variety of operating conditions are called automatic water level controls.
A dishwasher automatic water level control is disclosed in U.S. Pat. No. 3,415,261 wherein a pressure responsive switch in the lower sump area is used to detect when sufficient water is present in the dishwashing system to achieve a full pumping water pressure and terminate the water fill. Elevated air holes at the pump water inlet area result in the pump drawing partly air and cavitating until the sump water reaches the proper fill height.
A microprocessor based control circuit for washing appliances such as dishwashers and clothes washers is disclosed in U.S. Pat. No. 4,241,400 wherein a drain feedback switch is mechanically linked to a hinged diverter valve in the pump water flow path to detect when substantially all of the water has been discharged into the drain line. The electrical state of the drain feedback switch is input to the microprocessor to save or reallocate machine cycle time and facilitate detection of various drain fault conditions such as the failure to drain, slow drain or a plugged drain.
U.S. Pat. No. 3,777,232 discloses a circuit wherein the start winding of a motor is removed from the circuit on the basis of a phase difference between the main winding current and the applied voltage.