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]


// Copyright Contributors to the Open Shading Language project.
// SPDX-License-Identifier: BSD-3-Clause
// https://github.com/imageworks/OpenShadingLanguage


// Extensions to Imath classes for use in OSL's internals.
//
// The original Imath classes bear the "new BSD" license (same as
// ours above) and this copyright:
// Copyright (c) 2002, Industrial Light & Magic, a division of
// Lucas Digital Ltd. LLC.  All rights reserved.
// SPDX-License-Identifier: BSD-3-Clause


#pragma once

#include <OSL/oslconfig.h>


OSL_NAMESPACE_ENTER

// Choose to treat helper functions as static
// so their symbols don't escape and possibly collide
// with other compilation units who might be compiled with
// different compiler flags (like target ISA)

/// 3x3 matrix transforming a 3-vector.  This is curiously not supplied
/// by Imath, so we define it ourselves.
static OSL_FORCEINLINE OSL_HOSTDEVICE void
multMatrix (const Matrix33 &M, const Vec3 &src,
            Vec3 &dst)
{
    // Changed all Vec3 subscripts to access data members versus array casts
    auto a = src.x * M.x[0][0] + src.y * M.x[1][0] + src.z * M.x[2][0];
    auto b = src.x * M.x[0][1] + src.y * M.x[1][1] + src.z * M.x[2][1];
    auto c = src.x * M.x[0][2] + src.y * M.x[1][2] + src.z * M.x[2][2];
    dst.x = a;
    dst.y = b;
    dst.z = c;
}

// The current Imath::Matrix44<T>::multDirMatrix uses Imath::Vec3<T>::operator[] which
// causes correctness issues due to aliasing, so we have our own version to avoid it
static OSL_FORCEINLINE OSL_HOSTDEVICE void
multDirMatrix(const Matrix44 &M, const Vec3 &src, Vec3 &dst)
{
	auto a = src.x * M.x[0][0] + src.y * M.x[1][0] + src.z * M.x[2][0];
	auto b = src.x * M.x[0][1] + src.y * M.x[1][1] + src.z * M.x[2][1];
	auto c = src.x * M.x[0][2] + src.y * M.x[1][2] + src.z * M.x[2][2];

    dst.x = a;
    dst.y = b;
    dst.z = c;
}

//
// Inlinable version to enable vectorization
// Better results with return by value (versus taking reference parameter)
static OSL_FORCEINLINE OSL_HOSTDEVICE Vec3
multiplyDirByMatrix(const Matrix44 &M, const Vec3 &src)
{
	auto a = src.x * M.x[0][0] + src.y * M.x[1][0] + src.z * M.x[2][0];
	auto b = src.x * M.x[0][1] + src.y * M.x[1][1] + src.z * M.x[2][1];
	auto c = src.x * M.x[0][2] + src.y * M.x[1][2] + src.z * M.x[2][2];

    return Vec3(a,b,c);
}


/// Express dot product as a function rather than a method.
static OSL_FORCEINLINE OSL_HOSTDEVICE typename Vec2::BaseType
dot (const Vec2 &a, const Vec2 &b)
{
    return a.dot (b);
}


/// Express dot product as a function rather than a method.
static OSL_FORCEINLINE OSL_HOSTDEVICE typename Vec2::BaseType
dot (const Vec3 &a, const Vec3 &b)
{
    return a.dot (b);
}



/// Return the determinant of a 2x2 matrix.
static OSL_FORCEINLINE OSL_HOSTDEVICE typename Matrix22::BaseType
determinant (const Matrix22 &M)
{
    return M.x[0][0]*M.x[1][1] - M.x[0][1]*M.x[1][0];
}


static OSL_FORCEINLINE OSL_HOSTDEVICE void
makeIdentity(Matrix44 &m)
{
	using ScalarT = typename Matrix44::BaseType;
    // better allow SROA optimizations
    // by avoiding memset
    m.x[0][0] = ScalarT(1);
    m.x[0][1] = ScalarT(0);
    m.x[0][2] = ScalarT(0);
    m.x[0][3] = ScalarT(0);

    m.x[1][0] = ScalarT(0);
    m.x[1][1] = ScalarT(1);
    m.x[1][2] = ScalarT(0);
    m.x[1][3] = ScalarT(0);

    m.x[2][0] = ScalarT(0);
    m.x[2][1] = ScalarT(0);
    m.x[2][2] = ScalarT(1);
    m.x[2][3] = ScalarT(0);

    m.x[3][0] = ScalarT(0);
    m.x[3][1] = ScalarT(0);
    m.x[3][2] = ScalarT(0);
    m.x[3][3] = ScalarT(1);
}


// Partition general purpose inverse of Matrix44 into:
// test_if_affine
// affineInverse - fast path that is SIMD friendly
// nonAffineInverse - slow path to be used outside SIMD loop to
//                    handle any non-affine matrices
static OSL_FORCEINLINE bool test_if_affine(const Matrix44 & m) {
	using ScalarT = typename Matrix44::BaseType;
    return (m.x[0][3] == ScalarT(0)) &
           (m.x[1][3] == ScalarT(0)) &
           (m.x[2][3] == ScalarT(0)) &
           (m.x[3][3] == ScalarT(1));
}

static OSL_FORCEINLINE OSL_HOSTDEVICE Matrix44
affineInverse(const Matrix44 &m)
{
	using ScalarT = typename Matrix44::BaseType;
    // As we may speculatively call on non-affine matrices and just not use the result
    // we shouldn't bother verifying m is affine, just assume it and let caller non
    // use the results
    Matrix44 s (m.x[1][1] * m.x[2][2] - m.x[2][1] * m.x[1][2],
                m.x[2][1] * m.x[0][2] - m.x[0][1] * m.x[2][2],
                m.x[0][1] * m.x[1][2] - m.x[1][1] * m.x[0][2],
				ScalarT(0),

                m.x[2][0] * m.x[1][2] - m.x[1][0] * m.x[2][2],
                m.x[0][0] * m.x[2][2] - m.x[2][0] * m.x[0][2],
                m.x[1][0] * m.x[0][2] - m.x[0][0] * m.x[1][2],
				ScalarT(0),

                m.x[1][0] * m.x[2][1] - m.x[2][0] * m.x[1][1],
                m.x[2][0] * m.x[0][1] - m.x[0][0] * m.x[2][1],
                m.x[0][0] * m.x[1][1] - m.x[1][0] * m.x[0][1],
				ScalarT(0),

                ScalarT(0),
                ScalarT(0),
                ScalarT(0),
				ScalarT(1));

    auto r = m.x[0][0] * s.x[0][0] + m.x[0][1] * s.x[1][0] + m.x[0][2] * s.x[2][0];
    auto abs_r = IMATH_INTERNAL_NAMESPACE::abs (r);

    int may_have_divided_by_zero = 0;
    if (OSL_UNLIKELY(abs_r < ScalarT(1)))
    {
    	auto mr = abs_r / Imath::limits<ScalarT>::smallest();
#if 0
        OSL_PRAGMA(unroll)
        for (int i = 0; i < 3; ++i)
        {
            OSL_PRAGMA(unroll)
            for (int j = 0; j < 3; ++j)
            {
                if (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[i][j]))
                {
                    may_have_divided_by_zero = 1;
                }
            }
        }
#else
        // NOTE: using bitwise OR to avoid C++ semantics that cannot evaluate
        // the right hand side of logical OR unless left hand side is false
        if (
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[0][0])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[0][1])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[0][2])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[1][0])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[1][1])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[1][2])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[2][0])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[2][1])) |
            (mr <= IMATH_INTERNAL_NAMESPACE::abs (s.x[2][2]))
            ) {
            may_have_divided_by_zero = 1;
        }
#endif
    }

#if 0
    OSL_PRAGMA(unroll)
    for (int i = 0; i < 3; ++i)
    {
        OSL_PRAGMA(unroll)
        for (int j = 0; j < 3; ++j)
        {
            s.x[i][j] /= r;
        }
    }
#else
    // Just unroll by hand, about the same size as loop code
    // NOTE: opportunity to use reciprocal multiply here,
    // but that would affect the results, although compilers
    // might do that anyway based on optimization settings
    s.x[0][0] /= r;
    s.x[0][1] /= r;
    s.x[0][2] /= r;
    s.x[1][0] /= r;
    s.x[1][1] /= r;
    s.x[1][2] /= r;
    s.x[2][0] /= r;
    s.x[2][1] /= r;
    s.x[2][2] /= r;
#endif

    s.x[3][0] = -m.x[3][0] * s.x[0][0] - m.x[3][1] * s.x[1][0] - m.x[3][2] * s.x[2][0];
    s.x[3][1] = -m.x[3][0] * s.x[0][1] - m.x[3][1] * s.x[1][1] - m.x[3][2] * s.x[2][1];
    s.x[3][2] = -m.x[3][0] * s.x[0][2] - m.x[3][1] * s.x[1][2] - m.x[3][2] * s.x[2][2];

    if (OSL_UNLIKELY(may_have_divided_by_zero == 1))
    {
        makeIdentity(s);
    }
    return s;
}


// Avoid potential aliasing issues with OIIO implementation,
// but main purpose is to turn off FMA which can affect
// rounding and order of operations which can affect results
// with near 0 divisor.  Really only an issue when trying to
// match results between LLVM IR based implementation and
// compiler optimized versions which may have optimized
// differently than the LLVM IR version.
// Clang doesn't currently have a way to control fast-math/fp:strict
// at a per function level, so we will resort to disabling optimization
// for this function.  Not ideal, but this is already a slow path
// for exceptional situations.
// GCC could use __attribute__((optimize("-fno-fast-math")))
// NOTE:  only using "inline" to get ODR (One Definition Rule) behavior
static inline OSL_HOSTDEVICE Matrix44
nonAffineInverse(const Matrix44 &source) OSL_CLANG_ATTRIBUTE(optnone)
{
    OSL_INTEL_PRAGMA(float_control(strict,on,push))

	using ScalarT = typename Matrix44::BaseType;
    Matrix44 t(source);
    Matrix44 s;

    // Forward elimination

    for (int i = 0; i < 3 ; i++)
    {
        int pivot = i;

        ScalarT pivotsize = t.x[i][i];

        if (pivotsize < 0)
            pivotsize = -pivotsize;

        for (int j = i + 1; j < 4; j++)
        {
            ScalarT tmp = t.x[j][i];

            if (tmp < 0)
                tmp = -tmp;

            if (tmp > pivotsize)
            {
                pivot = j;
                pivotsize = tmp;
            }
        }

        if (pivotsize == 0)
        {
            return Matrix44();
        }

        if (pivot != i)
        {
            for (int j = 0; j < 4; j++)
            {
                ScalarT tmp;

                tmp = t.x[i][j];
                t.x[i][j] = t.x[pivot][j];
                t.x[pivot][j] = tmp;

                tmp = s.x[i][j];
                s.x[i][j] = s.x[pivot][j];
                s.x[pivot][j] = tmp;
            }
        }

        for (int j = i + 1; j < 4; j++)
        {
            ScalarT f = t.x[j][i] / t.x[i][i];

            for (int k = 0; k < 4; k++)
            {
                t.x[j][k] -= f * t.x[i][k];
                s.x[j][k] -= f * s.x[i][k];
            }
        }
    }

    // Backward substitution

    for (int i = 3; i >= 0; --i)
    {
        ScalarT f;

        if ((f = t.x[i][i]) == 0)
        {
            return Matrix44();
        }

        for (int j = 0; j < 4; j++)
        {
            t.x[i][j] /= f;
            s.x[i][j] /= f;
        }

        for (int j = 0; j < i; j++)
        {
            f = t.x[j][i];

            for (int k = 0; k < 4; k++)
            {
                t.x[j][k] -= f * t.x[i][k];
                s.x[j][k] -= f * s.x[i][k];
            }
        }
    }

    return s;
}


// In order to have inlinable Matrix44*float
// Override with a more specific version than
// template <class T>
// inline Matrix44<T>
// operator * (T a, const Matrix44<T> &v);

static OSL_FORCEINLINE OSL_HOSTDEVICE Matrix44
operator * (typename Matrix44::BaseType a, const Matrix44 &v)
{
    return Matrix44 (v.x[0][0] * a,
                     v.x[0][1] * a,
                     v.x[0][2] * a,
                     v.x[0][3] * a,
                     v.x[1][0] * a,
                     v.x[1][1] * a,
                     v.x[1][2] * a,
                     v.x[1][3] * a,
                     v.x[2][0] * a,
                     v.x[2][1] * a,
                     v.x[2][2] * a,
                     v.x[2][3] * a,
                     v.x[3][0] * a,
                     v.x[3][1] * a,
                     v.x[3][2] * a,
                     v.x[3][3] * a);
}

static OSL_FORCEINLINE OSL_HOSTDEVICE Matrix44
inlinedTransposed (const Matrix44 &m)
{
    return Matrix44 (m.x[0][0],
                     m.x[1][0],
                     m.x[2][0],
                     m.x[3][0],
                     m.x[0][1],
                     m.x[1][1],
                     m.x[2][1],
                     m.x[3][1],
                     m.x[0][2],
                     m.x[1][2],
                     m.x[2][2],
                     m.x[3][2],
                     m.x[0][3],
                     m.x[1][3],
                     m.x[2][3],
                     m.x[3][3]);
}

// Inlinable version to enable vectorization
// Better results with return by value (versus taking reference parameter)
static OSL_FORCEINLINE OSL_HOSTDEVICE Matrix44
multiplyMatrixByMatrix (const Matrix44 &a,
                       const Matrix44 &b)
{
    const auto a00 = a.x[0][0];
    const auto a01 = a.x[0][1];
    const auto a02 = a.x[0][2];
    const auto a03 = a.x[0][3];

    const auto c00  = a00 * b.x[0][0]  + a01 * b.x[1][0]  + a02 * b.x[2][0]  + a03 * b.x[3][0];
    const auto c01  = a00 * b.x[0][1]  + a01 * b.x[1][1]  + a02 * b.x[2][1]  + a03 * b.x[3][1];
    const auto c02  = a00 * b.x[0][2]  + a01 * b.x[1][2]  + a02 * b.x[2][2] + a03 * b.x[3][2];
    const auto c03  = a00 * b.x[0][3]  + a01 * b.x[1][3]  + a02 * b.x[2][3] + a03 * b.x[3][3];

    const auto a10 = a.x[1][0];
    const auto a11 = a.x[1][1];
    const auto a12 = a.x[1][2];
    const auto a13 = a.x[1][3];

    const auto c10  = a10 * b.x[0][0]  + a11 * b.x[1][0]  + a12 * b.x[2][0]  + a13 * b.x[3][0];
    const auto c11  = a10 * b.x[0][1]  + a11 * b.x[1][1]  + a12 * b.x[2][1]  + a13 * b.x[3][1];
    const auto c12  = a10 * b.x[0][2]  + a11 * b.x[1][2]  + a12 * b.x[2][2] + a13 * b.x[3][2];
    const auto c13  = a10 * b.x[0][3]  + a11 * b.x[1][3]  + a12 * b.x[2][3] + a13 * b.x[3][3];

    const auto a20 = a.x[2][0];
    const auto a21 = a.x[2][1];
    const auto a22 = a.x[2][2];
    const auto a23 = a.x[2][3];

    const auto c20  = a20 * b.x[0][0]  + a21 * b.x[1][0]  + a22 * b.x[2][0]  + a23 * b.x[3][0];
    const auto c21  = a20 * b.x[0][1]  + a21 * b.x[1][1]  + a22 * b.x[2][1]  + a23 * b.x[3][1];
    const auto c22 = a20 * b.x[0][2]  + a21 * b.x[1][2]  + a22 * b.x[2][2] + a23 * b.x[3][2];
    const auto c23 = a20 * b.x[0][3]  + a21 * b.x[1][3]  + a22 * b.x[2][3] + a23 * b.x[3][3];

    const auto a30 = a.x[3][0];
    const auto a31 = a.x[3][1];
    const auto a32 = a.x[3][2];
    const auto a33 = a.x[3][3];

    const auto c30 = a30 * b.x[0][0]  + a31 * b.x[1][0]  + a32 * b.x[2][0]  + a33 * b.x[3][0];
    const auto c31 = a30 * b.x[0][1]  + a31 * b.x[1][1]  + a32 * b.x[2][1]  + a33 * b.x[3][1];
    const auto c32 = a30 * b.x[0][2]  + a31 * b.x[1][2]  + a32 * b.x[2][2] + a33 * b.x[3][2];
    const auto c33 = a30 * b.x[0][3]  + a31 * b.x[1][3]  + a32 * b.x[2][3] + a33 * b.x[3][3];
    return Matrix44(
            c00, c01, c02, c03,
            c10, c11, c12, c13,
            c20, c21, c22, c23,
            c30, c31, c32, c33
        );

}

OSL_NAMESPACE_EXIT