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) 2015-2019, NVIDIA CORPORATION. All rights reserved.
 *
 * See LICENSE.txt for license information
 ************************************************************************/

#ifndef NCCL_COMMON_KERNEL_H_
#define NCCL_COMMON_KERNEL_H_

#include "devcomm.h"
#include <cstdio>
#include <cstdint>

#include <cuda_runtime.h>

// Define min for ssize_t
static __device__ int min(int a, ssize_t b) { return (a < b) ? a : b; }

typedef uint64_t PackType;

// unpack x and y to elements of type T and apply FUNC to each element
template<class FUNC, typename T>
struct MULTI {
  __device__ PackType operator()(const PackType x, const PackType y) const;
};

template<class FUNC>
struct MULTI<FUNC, int8_t> {
  static_assert(sizeof(PackType) == 2 * sizeof(uint32_t),
      "PackType must be twice the size of uint32_t.");
  union converter {
    PackType storage;
    struct {
      uint32_t a, b;
    };
  };

  __device__ PackType operator()(const PackType x, const PackType y) const {
    converter cx, cy, cr;
    cx.storage = x;
    cy.storage = y;

    // for char, we do these as vector ops
    cr.a = FUNC()(cx.a, cy.a);
    cr.b = FUNC()(cx.b, cy.b);

    return cr.storage;
  }
};

template<class FUNC>
struct MULTI<FUNC, uint8_t> {
  static_assert(sizeof(PackType) == 2 * sizeof(uint32_t),
      "PackType must be twice the size of uint32_t.");
  union converter {
    PackType storage;
    struct {
      uint32_t a, b;
    };
  };

  __device__ PackType operator()(const PackType x, const PackType y) const {
    converter cx, cy, cr;
    cx.storage = x;
    cy.storage = y;

    // for char, we do these as vector ops
    cr.a = FUNC()(cx.a, cy.a);
    cr.b = FUNC()(cx.b, cy.b);

    return cr.storage;
  }
};

template<class FUNC>
struct MULTI<FUNC, int32_t> {
  static_assert(sizeof(PackType) == 2 * sizeof(int32_t),
      "PackType must be twice the size of int.");
  union converter {
    PackType storage;
    struct {
      int32_t a, b;
    };
  };

  __device__ PackType operator()(const PackType x, const PackType y) const {
    converter cx, cy, cr;
    cx.storage = x;
    cy.storage = y;

    cr.a = FUNC()(cx.a, cy.a);
    cr.b = FUNC()(cx.b, cy.b);

    return cr.storage;
  }
};

template<class FUNC>
struct MULTI<FUNC, uint32_t> {
  static_assert(sizeof(PackType) == 2 * sizeof(uint32_t),
      "PackType must be twice the size of int.");
  union converter {
    PackType storage;
    struct {
      uint32_t a, b;
    };
  };

  __device__ PackType operator()(const PackType x, const PackType y) const {
    converter cx, cy, cr;
    cx.storage = x;
    cy.storage = y;

    cr.a = FUNC()(cx.a, cy.a);
    cr.b = FUNC()(cx.b, cy.b);

    return cr.storage;
  }
};

template<class FUNC>
struct MULTI<FUNC, half> {
  static_assert(sizeof(PackType) == 4 * sizeof(half),
      "PackType must be four times the size of half.");

  struct PackHalf2 {
    half2 a, b;
  };

  __device__ PackType operator()(const PackType x, const PackType y) const {
    struct PackHalf2 cx, cy, cr;
    cx = *(reinterpret_cast<const struct PackHalf2*>(&x));
    cy = *(reinterpret_cast<const struct PackHalf2*>(&y));

    cr.a = FUNC()(cx.a, cy.a);
    cr.b = FUNC()(cx.b, cy.b);

    return *(reinterpret_cast<PackType*>(&cr));
  }
};

template<class FUNC>
struct MULTI<FUNC, float> {
  static_assert(sizeof(PackType) == 2 * sizeof(float),
      "PackType must be twice the size of float.");
  union converter {
    PackType storage;
    struct {
      float a, b;
    };
  };

  __device__ PackType operator()(const PackType x, const PackType y) const {
    converter cx, cy, cr;
    cx.storage = x;
    cy.storage = y;

    cr.a = FUNC()(cx.a, cy.a);
    cr.b = FUNC()(cx.b, cy.b);

    return cr.storage;
  }
};

template<class FUNC>
struct MULTI<FUNC, double> {
  static_assert(sizeof(PackType) == sizeof(double),
      "PackType must be the same size as double.");
  __device__ PackType operator()(const PackType x, const PackType y) const {
    double rv = FUNC()(__longlong_as_double(x), __longlong_as_double(y));
    return __double_as_longlong(rv);
  }
};

template<class FUNC>
struct MULTI<FUNC, uint64_t> {
  static_assert(sizeof(PackType) == sizeof(uint64_t),
      "PackType must be the same size as uint64_t.");
  __device__ PackType operator()(const PackType x, const PackType y) const {
    uint64_t rv = FUNC()(x, y);
    return rv;
  }
};

template<class FUNC>
struct MULTI<FUNC, int64_t> {
  static_assert(sizeof(PackType) == sizeof(int64_t),
      "PackType must be the same size as int64_t.");
  __device__ PackType operator()(const PackType x, const PackType y) const {
    int64_t rv = FUNC()((int64_t)x, (int64_t)y);
    return rv;
  }
};

template<typename T> inline __device__
T vFetch(const volatile T* ptr) {
  return *ptr;
}

template<typename T> inline __device__
void vStore(volatile T* ptr, const T val) {
  *ptr = val;
}

#if CUDART_VERSION < 9000
template<> inline __device__
half vFetch<half>(const volatile half* ptr) {
  half r;
  r.x = ptr->x;
  return r;
}

template<> inline __device__
void vStore<half>(volatile half* ptr, const half val) {
  ptr->x = val.x;
}
#else
template<> inline __device__
half vFetch<half>(const volatile half* ptr) {
  half r;
  r = ((half*)ptr)[0];
  return r;
}

template<> inline __device__
void vStore<half>(volatile half* ptr, const half val) {
  ((half*)ptr)[0] = val;
}
#endif

typedef ulong2 Pack128;

template<class FUNC, typename T>
struct MULTI128 {
  __device__ void operator()(Pack128& x, Pack128& y) {
    x.x = MULTI<FUNC, T>()(x.x, y.x);
    x.y = MULTI<FUNC, T>()(x.y, y.y);
  }
};

inline __device__ void Fetch128(Pack128& v, const Pack128* p) {
  asm volatile("ld.volatile.global.v2.u64 {%0,%1}, [%2];" : "=l"(v.x), "=l"(v.y) : "l"(p) : "memory");
}
inline __device__ void Store128(Pack128* p, Pack128& v) {
  asm volatile("st.volatile.global.v2.u64 [%0], {%1,%2};" :: "l"(p), "l"(v.x), "l"(v.y) : "memory");
}

template<class FUNC, typename T, int MINSRCS, int MAXSRCS, int MINDSTS, int MAXDSTS>
__device__ __forceinline__ void ReduceCopyMulti(const int tid, const int nthreads,
    int nsrcs, const T* srcs[MAXSRCS], int ndsts, T* dsts[MAXDSTS],
    const int offset, const int N) {
  for (int idx = offset+tid; idx < offset+N; idx += nthreads) {
    T val = vFetch(srcs[0]+idx);
    #pragma unroll
    for (int i=1; i<MINSRCS; i++) val = FUNC()(val, vFetch(srcs[i]+idx));
    #pragma unroll 1
    for (int i=MINSRCS; i<MAXSRCS && i<nsrcs; i++) val = FUNC()(val, vFetch(srcs[i]+idx));

    #pragma unroll
    for (int i=0; i<MINDSTS; i++) vStore(dsts[i]+idx, val);
    #pragma unroll 1
    for (int i=MINDSTS; i<MAXDSTS && i<ndsts; i++) vStore(dsts[i]+idx, val);
  }
}

template<class FUNC, typename T, int UNROLL, int MINSRCS, int MAXSRCS, int MINDSTS, int MAXDSTS>
__device__ __forceinline__ void ReduceCopy128bMulti( const int w, const int nw, const int t,
    int nsrcs, const T* s[MAXSRCS], int ndsts, T* d[MAXDSTS],
    const int elemOffset, const int Npack) {
  const int inc = nw * UNROLL * WARP_SIZE;
  int offset = w * UNROLL * WARP_SIZE + t;

  const Pack128* srcs[MAXSRCS];
  for (int i=0; i<MAXSRCS; i++) srcs[i] = ((const Pack128*)(s[i]+elemOffset))+offset;
  Pack128* dsts[MAXDSTS];
  for (int i=0; i<MAXDSTS; i++) dsts[i] = ((Pack128*)(d[i]+elemOffset))+offset;

  while (offset < Npack) {
    Pack128 vals[UNROLL];
    // Load and reduce
    for (int u = 0; u < UNROLL; ++u) Fetch128(vals[u], srcs[0]+u*WARP_SIZE);

    for (int i=1; i<MINSRCS; i++) {
      Pack128 vals2[UNROLL];
      for (int u = 0; u < UNROLL; ++u) Fetch128(vals2[u], srcs[i]+u*WARP_SIZE);
      for (int u = 0; u < UNROLL; ++u) MULTI128<FUNC, T>()(vals[u], vals2[u]);
    }
    #pragma unroll 1
    for (int i=MINSRCS; i<MAXSRCS && i<nsrcs; i++) {
      Pack128 vals2[UNROLL];
      for (int u = 0; u < UNROLL; ++u) Fetch128(vals2[u], srcs[i]+u*WARP_SIZE);
      for (int u = 0; u < UNROLL; ++u) MULTI128<FUNC, T>()(vals[u], vals2[u]);
    }

    // Store
    for (int i = 0; i < MINDSTS; i++) {
      for (int u = 0; u < UNROLL; ++u) Store128(dsts[i]+u*WARP_SIZE, vals[u]);
    }
    #pragma unroll 1
    for (int i=MINDSTS; i<MAXDSTS && i<ndsts; i++) {
      for (int u = 0; u < UNROLL; ++u) Store128(dsts[i]+u*WARP_SIZE, vals[u]);
    }
    for (int i=0; i<MAXSRCS; i++) srcs[i] += inc;
    for (int i=0; i<MAXDSTS; i++) dsts[i] += inc;
    offset += inc;
  }
}

template <typename T>
__device__ int ptrAlign128(T* ptr) { return (uint64_t)ptr % alignof(Pack128); }

// Try to limit consecutive load/stores to 8.
// Use UNROLL 8 when we have a single source and a single destination, 4 otherwise
#define AUTOUNROLL (UNROLL*(4/(MINDSTS+MINSRCS)))

template<int UNROLL, class FUNC, typename T, int MINSRCS, int MAXSRCS, int MINDSTS, int MAXDSTS>
__device__ __forceinline__ void ReduceOrCopyMulti(const int tid, const int nthreads,
    int nsrcs, const T* srcs[MAXSRCS], int ndsts, T* dsts[MAXDSTS],
    int N) {
  int Nrem = N;
  if (Nrem <= 0) return;

  int alignDiff = 0;
  int align = ptrAlign128(srcs[0]);
  #pragma unroll
  for (int i=1; i<MINSRCS; i++) alignDiff |= (align ^ ptrAlign128(srcs[i]));
  for (int i=MINSRCS; i<MAXSRCS && i<nsrcs; i++) alignDiff |= (align ^ ptrAlign128(srcs[i]));
  #pragma unroll
  for (int i=0; i<MINDSTS; i++) alignDiff |= (align ^ ptrAlign128(dsts[i]));
  for (int i=MINDSTS; i<MAXDSTS && i<ndsts; i++) alignDiff |= (align ^ ptrAlign128(dsts[i]));

  int Npreamble = alignDiff ? Nrem :
    N < alignof(Pack128) ? N :
    (alignof(Pack128) - align) % alignof(Pack128);

  // stage 1: preamble: handle any elements up to the point of everything coming
  // into alignment
  if (Npreamble) {
    ReduceCopyMulti<FUNC, T, MINSRCS, MAXSRCS, MINDSTS, MAXDSTS>(tid, nthreads, nsrcs, srcs, ndsts, dsts, 0, Npreamble);
    Nrem -= Npreamble;
    if (Nrem == 0) return;
  }
  int offset = Npreamble;

  // stage 2: fast path: use 128b loads/stores to do the bulk of the work,
  // assuming the pointers we have are all 128-bit alignable.
  int w = tid / WARP_SIZE;       // Warp number
  int nw = nthreads / WARP_SIZE; // Number of warps
  int t = tid % WARP_SIZE;       // Thread (inside the warp)

  const int packFactor = sizeof(Pack128) / sizeof(T);

  // stage 2a: main loop
  int Npack2a = (Nrem / (packFactor * AUTOUNROLL * WARP_SIZE))
      * (AUTOUNROLL * WARP_SIZE); // round down
  int Nelem2a = Npack2a * packFactor;

  ReduceCopy128bMulti<FUNC, T, AUTOUNROLL, MINSRCS, MAXSRCS, MINDSTS, MAXDSTS>(w, nw, t, nsrcs, srcs, ndsts, dsts, offset, Npack2a);

  Nrem -= Nelem2a;
  if (Nrem == 0) return;
  offset += Nelem2a;

  // stage 2b: slightly less optimized for section when we don't have full
  // unrolling

  int Npack2b = Nrem / packFactor;
  int Nelem2b = Npack2b * packFactor;

  ReduceCopy128bMulti<FUNC, T, 1, MINSRCS, MAXSRCS, MINDSTS, MAXDSTS>(w, nw, t, nsrcs, srcs, ndsts, dsts, offset, Npack2b);

  Nrem -= Nelem2b;
  if (Nrem == 0) return;
  offset += Nelem2b;

  // stage 2c: tail
  ReduceCopyMulti<FUNC, T, MINSRCS, MAXSRCS, MINDSTS, MAXDSTS>(tid, nthreads, nsrcs, srcs, ndsts, dsts, offset, Nrem);
}

#endif // COMMON_KERNEL_H_