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 (C) 2011 Milo Yip
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

#ifndef RAPIDJSON_STRTOD_
#define RAPIDJSON_STRTOD_

#include "../rapidjson.h"
#include "ieee754.h"
#include "biginteger.h"
#include "diyfp.h"
#include "pow10.h"

RAPIDJSON_NAMESPACE_BEGIN
namespace internal {

inline double FastPath(double significand, int exp) {
    if (exp < -308)
        return 0.0;
    else if (exp >= 0)
        return significand * internal::Pow10(exp);
    else
        return significand / internal::Pow10(-exp);
}

inline double StrtodNormalPrecision(double d, int p) {
    if (p < -308) {
        // Prevent expSum < -308, making Pow10(p) = 0
        d = FastPath(d, -308);
        d = FastPath(d, p + 308);
    }
    else
        d = FastPath(d, p);
    return d;
}

template <typename T>
inline T Min3(T a, T b, T c) {
    T m = a;
    if (m > b) m = b;
    if (m > c) m = c;
    return m;
}

inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp, bool* adjustToNegative) {
    const Double db(b);
    const uint64_t bInt = db.IntegerSignificand();
    const int bExp = db.IntegerExponent();
    const int hExp = bExp - 1;

    int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;

    // Adjust for decimal exponent
    if (dExp >= 0) {
        dS_Exp2 += dExp;
        dS_Exp5 += dExp;
    }
    else {
        bS_Exp2 -= dExp;
        bS_Exp5 -= dExp;
        hS_Exp2 -= dExp;
        hS_Exp5 -= dExp;
    }

    // Adjust for binary exponent
    if (bExp >= 0)
        bS_Exp2 += bExp;
    else {
        dS_Exp2 -= bExp;
        hS_Exp2 -= bExp;
    }

    // Adjust for half ulp exponent
    if (hExp >= 0)
        hS_Exp2 += hExp;
    else {
        dS_Exp2 -= hExp;
        bS_Exp2 -= hExp;
    }

    // Remove common power of two factor from all three scaled values
    int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
    dS_Exp2 -= common_Exp2;
    bS_Exp2 -= common_Exp2;
    hS_Exp2 -= common_Exp2;

    BigInteger dS = d;
    dS.MultiplyPow5(dS_Exp5) <<= dS_Exp2;

    BigInteger bS(bInt);
    bS.MultiplyPow5(bS_Exp5) <<= bS_Exp2;

    BigInteger hS(1);
    hS.MultiplyPow5(hS_Exp5) <<= hS_Exp2;

    BigInteger delta(0);
    *adjustToNegative = dS.Difference(bS, &delta);

    int cmp = delta.Compare(hS);
    // If delta is within 1/2 ULP, check for special case when significand is power of two.
    // In this case, need to compare with 1/2h in the lower bound.
    if (cmp < 0 && *adjustToNegative && // within and dS < bS
        db.IsNormal() && (bInt & (bInt - 1)) == 0 && // Power of 2
        db.Uint64Value() != RAPIDJSON_UINT64_C2(0x00100000, 0x00000000)) // minimum normal number must not do this
    {
        delta <<= 1;
        return delta.Compare(hS);
    }
    return cmp;
}

inline bool StrtodFast(double d, int p, double* result) {
    // Use fast path for string-to-double conversion if possible
    // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
    if (p > 22  && p < 22 + 16) {
        // Fast Path Cases In Disguise
        d *= internal::Pow10(p - 22);
        p = 22;
    }

    if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
        *result = FastPath(d, p);
        return true;
    }
    else
        return false;
}

// Compute an approximation and see if it is within 1/2 ULP
inline bool StrtodDiyFp(const char* decimals, size_t length, size_t decimalPosition, int exp, double* result) {
    uint64_t significand = 0;
    size_t i = 0;   // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999    
    for (; i < length; i++) {
        if (significand  >  RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
            (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
            break;
        significand = significand * 10 + (decimals[i] - '0');
    }
    
    if (i < length && decimals[i] >= '5') // Rounding
        significand++;

    size_t remaining = length - i;
    const unsigned kUlpShift = 3;
    const unsigned kUlp = 1 << kUlpShift;
    int error = (remaining == 0) ? 0 : kUlp / 2;

    DiyFp v(significand, 0);
    v = v.Normalize();
    error <<= -v.e;

    const int dExp = (int)decimalPosition - (int)i + exp;

    int actualExp;
    DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
    if (actualExp != dExp) {
        static const DiyFp kPow10[] = {
            DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60),  // 10^1
            DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57),  // 10^2
            DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54),  // 10^3
            DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50),  // 10^4
            DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47),  // 10^5
            DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44),  // 10^6
            DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40)   // 10^7
        };
        int adjustment = dExp - actualExp - 1;
        RAPIDJSON_ASSERT(adjustment >= 0 && adjustment < 7);
        v = v * kPow10[adjustment];
        if (length + adjustment > 19) // has more digits than decimal digits in 64-bit
            error += kUlp / 2;
    }

    v = v * cachedPower;

    error += kUlp + (error == 0 ? 0 : 1);

    const int oldExp = v.e;
    v = v.Normalize();
    error <<= oldExp - v.e;

    const unsigned effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
    unsigned precisionSize = 64 - effectiveSignificandSize;
    if (precisionSize + kUlpShift >= 64) {
        unsigned scaleExp = (precisionSize + kUlpShift) - 63;
        v.f >>= scaleExp;
        v.e += scaleExp; 
        error = (error >> scaleExp) + 1 + kUlp;
        precisionSize -= scaleExp;
    }

    DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
    const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
    const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
    if (precisionBits >= halfWay + error)
        rounded.f++;

    *result = rounded.ToDouble();

    return halfWay - error >= precisionBits || precisionBits >= halfWay + error;
}

inline double StrtodBigInteger(double approx, const char* decimals, size_t length, size_t decimalPosition, int exp) {
    const BigInteger dInt(decimals, length);
    const int dExp = (int)decimalPosition - (int)length + exp;
    Double a(approx);
    for (int i = 0; i < 10; i++) {
        bool adjustToNegative;
        int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp, &adjustToNegative);
        if (cmp < 0)
            return a.Value();  // within half ULP
        else if (cmp == 0) {
            // Round towards even
            if (a.Significand() & 1)
                return adjustToNegative ? a.PreviousPositiveDouble() : a.NextPositiveDouble();
            else
                return a.Value();
        }
        else // adjustment
            a = adjustToNegative ? a.PreviousPositiveDouble() : a.NextPositiveDouble();
    }

    // This should not happen, but in case there is really a bug, break the infinite-loop
    return a.Value();
}

inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
    RAPIDJSON_ASSERT(d >= 0.0);
    RAPIDJSON_ASSERT(length >= 1);

    double result;
    if (StrtodFast(d, p, &result))
        return result;

    // Trim leading zeros
    while (*decimals == '0' && length > 1) {
        length--;
        decimals++;
        decimalPosition--;
    }

    // Trim trailing zeros
    while (decimals[length - 1] == '0' && length > 1) {
        length--;
        decimalPosition--;
        exp++;
    }

    // Trim right-most digits
    const int kMaxDecimalDigit = 780;
    if ((int)length > kMaxDecimalDigit) {
        exp += (int(length) - kMaxDecimalDigit);
        length = kMaxDecimalDigit;
    }

    // If too small, underflow to zero
    if (int(length) + exp < -324)
        return 0.0;

    if (StrtodDiyFp(decimals, length, decimalPosition, exp, &result))
        return result;

    // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
    return StrtodBigInteger(result, decimals, length, decimalPosition, exp);
}

} // namespace internal
RAPIDJSON_NAMESPACE_END

#endif // RAPIDJSON_STRTOD_