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]


/**************************************************************************

  File: Physics1.h  

  Prepared by Erkin Tunca for nehe.gamedev.net

**************************************************************************/

#include <math.h>

// class Vector3D		---> An object to represent a 3D vector or a 3D point in space
class Vector3D
{
public:
	float x;									// the x value of this Vector3D
	float y;									// the y value of this Vector3D
	float z;									// the z value of this Vector3D

	Vector3D()									// Constructor to set x = y = z = 0
	{
		x = 0;
		y = 0;
		z = 0;
	}

	Vector3D(float x, float y, float z)			// Constructor that initializes this Vector3D to the intended values of x, y and z
	{
		this->x = x;
		this->y = y;
		this->z = z;
	}

	Vector3D& operator= (Vector3D v)			// operator= sets values of v to this Vector3D. example: v1 = v2 means that values of v2 are set onto v1
	{
		x = v.x;
		y = v.y;
		z = v.z;
		return *this;
	}

	Vector3D operator+ (Vector3D v)				// operator+ is used to add two Vector3D's. operator+ returns a new Vector3D
	{
		return Vector3D(x + v.x, y + v.y, z + v.z);
	}

	Vector3D operator- (Vector3D v)				// operator- is used to take difference of two Vector3D's. operator- returns a new Vector3D
	{
		return Vector3D(x - v.x, y - v.y, z - v.z);
	}

	Vector3D operator* (float value)			// operator* is used to scale a Vector3D by a value. This value multiplies the Vector3D's x, y and z.
	{
		return Vector3D(x * value, y * value, z * value);
	}

	Vector3D operator/ (float value)			// operator/ is used to scale a Vector3D by a value. This value divides the Vector3D's x, y and z.
	{
		return Vector3D(x / value, y / value, z / value);
	}

	Vector3D& operator+= (Vector3D v)			// operator+= is used to add another Vector3D to this Vector3D.
	{
		x += v.x;
		y += v.y;
		z += v.z;
		return *this;
	}

	Vector3D& operator-= (Vector3D v)			// operator-= is used to subtract another Vector3D from this Vector3D.
	{
		x -= v.x;
		y -= v.y;
		z -= v.z;
		return *this;
	}

	Vector3D& operator*= (float value)			// operator*= is used to scale this Vector3D by a value.
	{
		x *= value;
		y *= value;
		z *= value;
		return *this;
	}

	Vector3D& operator/= (float value)			// operator/= is used to scale this Vector3D by a value.
	{
		x /= value;
		y /= value;
		z /= value;
		return *this;
	}


	Vector3D operator- ()						// operator- is used to set this Vector3D's x, y, and z to the negative of them.
	{
		return Vector3D(-x, -y, -z);
	}

	float length()								// length() returns the length of this Vector3D
	{
		return sqrtf(x*x + y*y + z*z);
	};

	void unitize()								// unitize() normalizes this Vector3D that its direction remains the same but its length is 1.
	{
		float length = this->length();

		if (length == 0)
			return;

		x /= length;
		y /= length;
		z /= length;
	}

	Vector3D unit()								// unit() returns a new Vector3D. The returned value is a unitized version of this Vector3D.
	{
		float length = this->length();

		if (length == 0)
			return *this;
		
		return Vector3D(x / length, y / length, z / length);
	}

};

// class Mass			---> An object to represent a mass
class Mass
{
public:
	float m;									// The mass value
	Vector3D pos;								// Position in space
	Vector3D vel;								// Velocity
	Vector3D force;								// Force applied on this mass at an instance

	Mass(float m)								// Constructor
	{
		this->m = m;
	}

	/*
	  void applyForce(Vector3D force) method is used to add external force to the mass. 
	  At an instance in time, several sources of force might affect the mass. The vector sum 
	  of these forces make up the net force applied to the mass at the instance.
	*/
	void applyForce(Vector3D force)
	{
		this->force += force;					// The external force is added to the force of the mass
	}

	/*
	  void init() method sets the force values to zero
	*/
	void init()
	{
		force.x = 0;
		force.y = 0;
		force.z = 0;
	}

	/*
	  void simulate(float dt) method calculates the new velocity and new position of 
	  the mass according to change in time (dt). Here, a simulation method called
	  "The Euler Method" is used. The Euler Method is not always accurate, but it is 
	  simple. It is suitable for most of physical simulations that we know in common 
	  computer and video games.
	*/
	void simulate(float dt)
	{
		vel += (force / m) * dt;				// Change in velocity is added to the velocity.
												// The change is proportinal with the acceleration (force / m) and change in time

		pos += vel * dt;						// Change in position is added to the position.
												// Change in position is velocity times the change in time
	}

};

// class Simulation		---> A container object for simulating masses
class Simulation
{
public:
	int numOfMasses;								// number of masses in this container
	Mass** masses;									// masses are held by pointer to pointer. (Here Mass** represents a 1 dimensional array)
	
	Simulation(int numOfMasses, float m)			// Constructor creates some masses with mass values m
	{
		this->numOfMasses = numOfMasses;
		
		masses = new Mass*[numOfMasses];			// Create an array of pointers

		for (int count = 0; count < numOfMasses; ++count)		// We will step to every pointer in the array
			masses[count] = new Mass(m);				// Create a Mass as a pointer and put it in the array
	}

	virtual void release()							// delete the masses created
	{
		for (int count = 0; count < numOfMasses; ++count)		// we will delete all of them
		{
			delete(masses[count]);
			masses[count] = NULL;
		}

		delete(masses);
		masses = NULL;
	}

	Mass* getMass(int index)
	{
		if (index < 0 || index >= numOfMasses)		// if the index is not in the array
			return NULL;							// then return NULL

		return masses[index];						// get the mass at the index
	}

	virtual void init()								// this method will call the init() method of every mass
	{
		for (int count = 0; count < numOfMasses; ++count)		// We will init() every mass
			masses[count]->init();						// call init() method of the mass
	}

	virtual void solve()							// no implementation because no forces are wanted in this basic container
	{
													// in advanced containers, this method will be overrided and some forces will act on masses
	}

	virtual void simulate(float dt)					// Iterate the masses by the change in time
	{
		for (int count = 0; count < numOfMasses; ++count)		// We will iterate every mass
			masses[count]->simulate(dt);				// Iterate the mass and obtain new position and new velocity
	}

	virtual void operate(float dt)					// The complete procedure of simulation
	{
		init();										// Step 1: reset forces to zero
		solve();									// Step 2: apply forces
		simulate(dt);								// Step 3: iterate the masses by the change in time
	}

};

/*
  class ConstantVelocity is derived from class Simulation
  It creates 1 mass with mass value 1 kg and sets its velocity to (1.0f, 0.0f, 0.0f)
  so that the mass moves in the x direction with 1 m/s velocity.
*/
class ConstantVelocity : public Simulation
{
public:
	ConstantVelocity() : Simulation(1, 1.0f)				//Constructor firstly constructs its super class with 1 mass and 1 kg
	{
		masses[0]->pos = Vector3D(0.0f, 0.0f, 0.0f);		//a mass was created and we set its position to the origin
		masses[0]->vel = Vector3D(1.0f, 0.0f, 0.0f);		//we set the mass's velocity to (1.0f, 0.0f, 0.0f)
	}

};

/*
  class MotionUnderGravitation is derived from class Simulation
  It creates 1 mass with mass value 1 kg and sets its velocity to (10.0f, 15.0f, 0.0f) and its position to
  (-10.0f, 0.0f, 0.0f). The purpose of this application is to apply a gravitational force to the mass and
  observe the path it follows. The above velocity and position provides a fine projectile path with a
  9.81 m/s/s downward gravitational acceleration. 9.81 m/s/s is a very close value to the gravitational
  acceleration we experience on the earth.
*/
class MotionUnderGravitation : public Simulation
{
public:
	Vector3D gravitation;													//the gravitational acceleration

	MotionUnderGravitation(Vector3D gravitation) : Simulation(1, 1.0f)		//Constructor firstly constructs its super class with 1 mass and 1 kg
	{																		//Vector3D gravitation, is the gravitational acceleration
		this->gravitation = gravitation;									//set this class's gravitation
		masses[0]->pos = Vector3D(-10.0f, 0.0f, 0.0f);						//set the position of the mass
		masses[0]->vel = Vector3D(10.0f, 15.0f, 0.0f);						//set the velocity of the mass
	}

	virtual void solve()													//gravitational force will be applied therefore we need a "solve" method.
	{
		for (int a = 0; a < numOfMasses; ++a)								//we will apply force to all masses (actually we have 1 mass, but we can extend it in the future)
			masses[a]->applyForce(gravitation * masses[a]->m);				//gravitational force is as F = m * g. (mass times the gravitational acceleration)
	}
	
};

/*
  class MassConnectedWithSpring is derived from class Simulation
  It creates 1 mass with mass value 1 kg and binds the mass to an arbitrary constant point with a spring. 
  This point is refered as the connectionPos and the spring has a springConstant value to represent its 
  stiffness.
*/
class MassConnectedWithSpring : public Simulation
{
public:
	float springConstant;													//more the springConstant, stiffer the spring force
	Vector3D connectionPos;													//the arbitrary constant point that the mass is connected

	MassConnectedWithSpring(float springConstant) : Simulation(1, 1.0f)		//Constructor firstly constructs its super class with 1 mass and 1 kg
	{
		this->springConstant = springConstant;								//set the springConstant

		connectionPos = Vector3D(0.0f, -5.0f, 0.0f);						//set the connectionPos

		masses[0]->pos = connectionPos + Vector3D(10.0f, 0.0f, 0.0f);		//set the position of the mass 10 meters to the right side of the connectionPos
		masses[0]->vel = Vector3D(0.0f, 0.0f, 0.0f);						//set the velocity of the mass to zero
	}

	virtual void solve()													//the spring force will be applied
	{
		for (int count = 0; count < numOfMasses; ++count)								//we will apply force to all masses (actually we have 1 mass, but we can extend it in the future)
		{
			Vector3D springVector = masses[count]->pos - connectionPos;			//find a vector from the position of the mass to the connectionPos
			masses[count]->applyForce(-springVector * springConstant);			//apply the force according to the famous spring force formulation
		}
	}

};