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]


/**
 * KnotMesh.java
 *
 * Copyright (c) 2013-2016, F(X)yz
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *     * Redistributions of source code must retain the above copyright
 * notice, this list of conditions and the following disclaimer.
 *     * Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions and the following disclaimer in the
 * documentation and/or other materials provided with the distribution.
 *     * Neither the name of F(X)yz, any associated website, nor the
 * names of its contributors may be used to endorse or promote products
 * derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL F(X)yz BE LIABLE FOR ANY
 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */ 

package org.fxyz3d.shapes.primitives;

import javafx.beans.property.DoubleProperty;
import javafx.beans.property.IntegerProperty;
import javafx.beans.property.SimpleDoubleProperty;
import javafx.beans.property.SimpleIntegerProperty;
import javafx.scene.DepthTest;
import javafx.scene.shape.CullFace;
import javafx.scene.shape.DrawMode;
import javafx.scene.shape.TriangleMesh;
import org.fxyz3d.geometry.Face3;
import org.fxyz3d.geometry.Point3D;
import org.fxyz3d.shapes.primitives.helper.KnotHelper;

/**
 *  Spring based on this model:  http://en.wikipedia.org/wiki/Trefoil_knot
 *  Wrapped around a torus: http://mathoverflow.net/a/91459
    *  Using Frenet-Serret trihedron: http://mathematica.stackexchange.com/a/18612
 */
public class KnotMesh extends TexturedMesh {

    private static final double DEFAULT_MAJOR_RADIUS = 2.0D;
    private static final double DEFAULT_MINOR_RADIUS = 1.0D;
    private static final double DEFAULT_WIRE_RADIUS = 0.2D;
    private static final double DEFAULT_P = 2.0D; 
    private static final double DEFAULT_Q = 3.0D; 
    private static final double DEFAULT_LENGTH = 2.0D*Math.PI*DEFAULT_Q; 
    
    private static final int DEFAULT_LENGTH_DIVISIONS = 200;
    private static final int DEFAULT_WIRE_DIVISIONS = 50;
    private static final int DEFAULT_LENGTH_CROP = 0;
    private static final int DEFAULT_WIRE_CROP = 0;
    
    private static final double DEFAULT_START_ANGLE = 0.0D;
    private static final double DEFAULT_X_OFFSET = 0.0D;
    private static final double DEFAULT_Y_OFFSET = 0.0D;
    private static final double DEFAULT_Z_OFFSET = 1.0D;
    
    private KnotHelper knot;
    
    public KnotMesh() {
        this(DEFAULT_MAJOR_RADIUS, DEFAULT_MINOR_RADIUS, DEFAULT_WIRE_RADIUS, DEFAULT_P, DEFAULT_Q,
             DEFAULT_LENGTH_DIVISIONS, DEFAULT_WIRE_DIVISIONS, DEFAULT_LENGTH_CROP, DEFAULT_WIRE_CROP);
    }

    public KnotMesh(double majorRadius, double minorRadius, double wireRadius, double p, double q) {
        this(majorRadius, minorRadius, wireRadius, p, q, 
             DEFAULT_LENGTH_DIVISIONS, DEFAULT_WIRE_DIVISIONS, DEFAULT_LENGTH_CROP, DEFAULT_WIRE_CROP);
    }

    public KnotMesh(double majorRadius, double minorRadius, double wireRadius, double p, double q, 
                      int lengthDivisions, int wireDivisions, int lengthCrop, int wireCrop) {
        
        setMajorRadius(majorRadius);
        setMinorRadius(minorRadius);
        setWireRadius(wireRadius);
        setP(p);
        setQ(q);
        setLengthDivisions(lengthDivisions);
        setWireDivisions(wireDivisions);
        setLengthCrop(lengthCrop);
        setWireCrop(wireCrop);
        
        updateMesh();
        setCullFace(CullFace.BACK);
        setDrawMode(DrawMode.FILL);
        setDepthTest(DepthTest.ENABLE);
    }

    @Override
    protected final void updateMesh(){   
        setMesh(null);
        mesh=createKnot((float) getMajorRadius(), (float) getMinorRadius(), (float) getWireRadius(), (float) getP(), (float) getQ(), (float) getLength(),
            getLengthDivisions(), getWireDivisions(), getLengthCrop(), getWireCrop(),
            (float) getTubeStartAngleOffset(), (float)getxOffset(),(float)getyOffset(), (float)getzOffset());
        setMesh(mesh);
    }
    
    private final DoubleProperty majorRadius = new SimpleDoubleProperty(DEFAULT_MAJOR_RADIUS){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final double getMajorRadius() {
        return majorRadius.get();
    }

    public final void setMajorRadius(double value) {
        majorRadius.set(value);
    }

    public DoubleProperty majorRadiusProperty() {
        return majorRadius;
    }

    private final DoubleProperty minorRadius = new SimpleDoubleProperty(DEFAULT_MINOR_RADIUS){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final double getMinorRadius() {
        return minorRadius.get();
    }

    public final void setMinorRadius(double value) {
        minorRadius.set(value);
    }

    public DoubleProperty minorRadiusProperty() {
        return minorRadius;
    }
    
    private final DoubleProperty wireRadius = new SimpleDoubleProperty(DEFAULT_WIRE_RADIUS){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final double getWireRadius() {
        return wireRadius.get();
    }

    public final void setWireRadius(double value) {
        wireRadius.set(value);
    }

    public DoubleProperty wireRadiusProperty() {
        return wireRadius;
    }

    private final DoubleProperty length = new SimpleDoubleProperty(DEFAULT_LENGTH){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final double getLength() {
        return length.get();
    }

    public final void setLength(double value) {
        length.set(value);
    }

    public DoubleProperty lengthProperty() {
        return length;
    }

    private final DoubleProperty q = new SimpleDoubleProperty(DEFAULT_Q){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final double getQ() {
        return q.get();
    }

    public final void setQ(double value) {
        setLength(2d*Math.PI*Math.abs(value));
        q.set(value);
    }

    public DoubleProperty qProperty() {
        return q;
    }
    private final DoubleProperty p = new SimpleDoubleProperty(DEFAULT_P){
        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public double getP() {
        return p.get();
    }

    public final void setP(double value) {
        p.set(value);
    }

    public DoubleProperty pProperty() {
        return p;
    }
    
    private final IntegerProperty lengthDivisions = new SimpleIntegerProperty(DEFAULT_LENGTH_DIVISIONS){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final int getLengthDivisions() {
        return lengthDivisions.get();
    }

    public final void setLengthDivisions(int value) {
        lengthDivisions.set(value);
    }

    public IntegerProperty lengthDivisionsProperty() {
        return lengthDivisions;
    }

    private final IntegerProperty wireDivisions = new SimpleIntegerProperty(DEFAULT_WIRE_DIVISIONS){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final int getWireDivisions() {
        return wireDivisions.get();
    }

    public final void setWireDivisions(int value) {
        wireDivisions.set(value);
    }

    public IntegerProperty wireDivisionsProperty() {
        return wireDivisions;
    }

    private final IntegerProperty lengthCrop = new SimpleIntegerProperty(DEFAULT_LENGTH_CROP){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };
    
    public final int getLengthCrop() {
        return lengthCrop.get();
    }

    public final void setLengthCrop(int value) {
        lengthCrop.set(value);
    }

    public IntegerProperty lengthCropProperty() {
        return lengthCrop;
    }

    private final IntegerProperty wireCrop = new SimpleIntegerProperty(DEFAULT_WIRE_CROP){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };
    
    public final int getWireCrop() {
        return wireCrop.get();
    }

    public final void setWireCrop(int value) {
        wireCrop.set(value);
    }

    public IntegerProperty wireCropProperty() {
        return wireCrop;
    }
    
    private final DoubleProperty tubeStartAngleOffset = new SimpleDoubleProperty(DEFAULT_START_ANGLE){

        @Override protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
    };

    public final double getTubeStartAngleOffset() {
        return tubeStartAngleOffset.get();
    }

    public void setTubeStartAngleOffset(double value) {
        tubeStartAngleOffset.set(value);
    }

    public DoubleProperty tubeStartAngleOffsetProperty() {
        return tubeStartAngleOffset;
    }
    private final DoubleProperty xOffset = new SimpleDoubleProperty(DEFAULT_X_OFFSET){

        @Override
        protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
        
    };

    public final double getxOffset() {
        return xOffset.get();
    }

    public void setxOffset(double value) {
        xOffset.set(value);
    }

    public DoubleProperty xOffsetProperty() {
        return xOffset;
    }
    private final DoubleProperty yOffset = new SimpleDoubleProperty(DEFAULT_Y_OFFSET){

        @Override
        protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
        
    };

    public final double getyOffset() {
        return yOffset.get();
    }

    public void setyOffset(double value) {
        yOffset.set(value);
    }

    public DoubleProperty yOffsetProperty() {
        return yOffset;
    }
    private final DoubleProperty zOffset = new SimpleDoubleProperty(DEFAULT_Z_OFFSET){

        @Override
        protected void invalidated() {
            if(mesh!=null){
                updateMesh();
            }
        }
        
    };

    public final double getzOffset() {
        return zOffset.get();
    }

    public void setzOffset(double value) {
        zOffset.set(value);
    }

    public DoubleProperty zOffsetProperty() {
        return zOffset;
    }
    
    private TriangleMesh createKnot(float majorRadius, float minorRadius, float wireRadius, float p, float q, float length, 
            int subDivLength, int subDivWire, int cropLength, int cropWire,
            float startAngle, float xOffset, float yOffset, float zOffset) {
 
        listVertices.clear();
        listTextures.clear();
        listFaces.clear();
        
        int numDivWire = subDivWire + 1-2*cropWire;
        double a=wireRadius;
        
        knot = new KnotHelper(majorRadius, minorRadius, p, q);
        areaMesh.setWidth(knot.getLength());
        areaMesh.setHeight(polygonalSize(wireRadius));
        
        knot.calculateTrihedron(subDivLength);
        for (int t = cropLength; t <= subDivLength-cropLength; t++) {  // 0 - length
            for (int u = cropWire; u <= subDivWire-cropWire; u++) { // -Pi - +Pi
                if(cropWire>0 || (cropWire==0 && u<subDivWire)){
                    float du = (float) (((double)u)*2d*Math.PI / ((double)subDivWire));
                    double pol = polygonalSection(du);
                    float cu=(float)(a*pol*Math.cos(du)), su=(float)(a*pol*Math.sin(du)); 
                    listVertices.add(knot.getS(t, cu, su));
                }
            }
        }
        
        // Create texture coordinates
        createReverseTexCoords(subDivLength-2*cropLength,subDivWire-2*cropWire);
        
        // Create textures
        for (int t = cropLength; t < subDivLength-cropLength; t++) { // 0 - length
            for (int u = cropWire; u < subDivWire-cropWire; u++) { // -Pi - +Pi
                int p00 = (u-cropWire) + (t-cropLength)* numDivWire;
                int p01 = p00 + 1;
                int p10 = p00 + numDivWire;
                int p11 = p10 + 1;
                listTextures.add(new Face3(p00,p01,p11));
                listTextures.add(new Face3(p11,p10,p00));            
            }
        }
        
        // Create faces
        for (int t = cropLength; t < subDivLength-cropLength; t++) { // 0 - length
            for (int u = cropWire; u < subDivWire-cropWire; u++) { // -Pi - +Pi
                int p00 = (u-cropWire) + (t-cropLength)* (cropWire==0?subDivWire:numDivWire);
                int p01 = p00 + 1;
                int p10 = p00 + (cropWire==0?subDivWire:numDivWire);
                int p11 = p10 + 1;
                if(cropWire==0 && u==subDivWire-1){
                    p01-=subDivWire;
                    p11-=subDivWire;
                }
                listFaces.add(new Face3(p00,p01,p11));
                listFaces.add(new Face3(p11,p10,p00));            
            }
        }
        
        return createMesh();
    }
    
    public Point3D getPositionAt(double t){
        return knot.getPositionAt(t);
    }
    
    public Point3D getTangentAt(double t){
        return knot.getTangentAt(t);
    }
    
    public double getTau(double t){
        return knot.getTau(t);
    }
    
    public double getKappa(double t){
        return knot.getKappa(t);
    }
}