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]


// Mantid Repository : https://github.com/mantidproject/mantid
//
// Copyright &copy; 2018 ISIS Rutherford Appleton Laboratory UKRI,
//   NScD Oak Ridge National Laboratory, European Spallation Source,
//   Institut Laue - Langevin & CSNS, Institute of High Energy Physics, CAS
// SPDX - License - Identifier: GPL - 3.0 +
#include "MantidAlgorithms/UnwrapSNS.h"
#include "MantidAPI/HistogramValidator.h"
#include "MantidAPI/InstrumentValidator.h"
#include "MantidAPI/RawCountValidator.h"
#include "MantidAPI/SpectrumInfo.h"
#include "MantidAPI/WorkspaceFactory.h"
#include "MantidAPI/WorkspaceUnitValidator.h"
#include "MantidDataObjects/EventList.h"
#include "MantidGeometry/Instrument.h"
#include "MantidKernel/BoundedValidator.h"
#include "MantidKernel/CompositeValidator.h"
#include "MantidKernel/PhysicalConstants.h"
#include "MantidKernel/UnitFactory.h"

#include <limits>

namespace Mantid {
namespace Algorithms {

DECLARE_ALGORITHM(UnwrapSNS)

using namespace Kernel;
using namespace API;
using DataObjects::EventWorkspace;
using std::size_t;

/// Default constructor
UnwrapSNS::UnwrapSNS()
    : m_conversionConstant(0.), m_inputWS(), m_inputEvWS(), m_LRef(0.),
      m_Tmin(0.), m_Tmax(0.), m_frameWidth(0.), m_numberOfSpectra(0),
      m_XSize(0) {}

/// Initialisation method
void UnwrapSNS::init() {
  auto wsValidator = std::make_shared<CompositeValidator>();
  wsValidator->add<WorkspaceUnitValidator>("TOF");
  wsValidator->add<HistogramValidator>();
  wsValidator->add<RawCountValidator>();
  wsValidator->add<InstrumentValidator>();
  declareProperty(std::make_unique<WorkspaceProperty<MatrixWorkspace>>(
                      "InputWorkspace", "", Direction::Input, wsValidator),
                  "Contains numbers counts against time of flight (TOF).");
  declareProperty(std::make_unique<WorkspaceProperty<MatrixWorkspace>>(
                      "OutputWorkspace", "", Direction::Output),
                  "This workspace will be in the units of time of flight. (See "
                  "http://www.mantidproject.org/Units)");

  auto validator = std::make_shared<BoundedValidator<double>>();
  validator->setLower(0.01);
  declareProperty("LRef", 0.0, validator,
                  "A distance at which it is possible to deduce if a particle "
                  "is from the current or a past frame based on its arrival "
                  "time. This time criterion can be set with the property "
                  "below e.g. correct when arrival time < Tmin.");
  validator->setLower(0.01);
  declareProperty("Tmin", Mantid::EMPTY_DBL(), validator,
                  "With LRef this defines the maximum speed expected for "
                  "particles. For each count or time bin the mean particle "
                  "speed is calculated and if this is greater than LRef/Tmin "
                  "its TOF is corrected.");
  validator->setLower(0.01);
  declareProperty("Tmax", Mantid::EMPTY_DBL(), validator,
                  "The maximum time of flight of the data used for the width "
                  "of the frame. If not set the maximum time of flight of the "
                  "data is used.");

  // Calculate and set the constant factor for the conversion to wavelength
  const double TOFisinMicroseconds = 1e6;
  const double toAngstroms = 1e10;
  m_conversionConstant = (PhysicalConstants::h * toAngstroms) /
                         (PhysicalConstants::NeutronMass * TOFisinMicroseconds);
}

/** Executes the algorithm
 *  @throw std::runtime_error if the workspace is invalid or a child algorithm
 *fails
 *  @throw Kernel::Exception::InstrumentDefinitionError if detector, source or
 *sample positions cannot be calculated
 *
 */
void UnwrapSNS::exec() {
  // Get the input workspace
  m_inputWS = getProperty("InputWorkspace");

  // Get the "reference" flightpath (currently passed in as a property)
  m_LRef = getProperty("LRef");

  m_XSize = static_cast<int>(m_inputWS->x(0).size());
  m_numberOfSpectra = static_cast<int>(m_inputWS->getNumberHistograms());
  g_log.debug() << "Number of spectra in input workspace: " << m_numberOfSpectra
                << "\n";

  // go off and do the event version if appropriate
  m_inputEvWS = std::dynamic_pointer_cast<const EventWorkspace>(m_inputWS);
  if ((m_inputEvWS != nullptr)) // && ! this->getProperty("ForceHist")) // TODO
                                // remove ForceHist option
  {
    this->execEvent();
    return;
  }

  this->getTofRangeData(false);

  // set up the progress bar
  m_progress = std::make_unique<Progress>(this, 0.0, 1.0, m_numberOfSpectra);

  MatrixWorkspace_sptr outputWS = getProperty("OutputWorkspace");
  if (outputWS != m_inputWS) {
    outputWS = WorkspaceFactory::Instance().create(m_inputWS, m_numberOfSpectra,
                                                   m_XSize, m_XSize - 1);
    setProperty("OutputWorkspace", outputWS);
  }

  // without the primary flight path the algorithm cannot work
  const auto &spectrumInfo = m_inputWS->spectrumInfo();
  const double L1 = spectrumInfo.l1();

  PARALLEL_FOR_IF(Kernel::threadSafe(*m_inputWS, *outputWS))
  for (int workspaceIndex = 0; workspaceIndex < m_numberOfSpectra;
       workspaceIndex++) {
    PARALLEL_START_INTERUPT_REGION
    if (!spectrumInfo.hasDetectors(workspaceIndex)) {
      // If the detector flightpath is missing, zero the data
      g_log.debug() << "Detector information for workspace index "
                    << workspaceIndex << " is not available.\n";
      outputWS->setSharedX(workspaceIndex, m_inputWS->sharedX(workspaceIndex));
      outputWS->mutableY(workspaceIndex) = 0.0;
      outputWS->mutableE(workspaceIndex) = 0.0;
    } else {
      const double Ld = L1 + spectrumInfo.l2(workspaceIndex);
      // fix the x-axis
      std::vector<double> timeBins;
      size_t pivot = this->unwrapX(m_inputWS->x(workspaceIndex), timeBins, Ld);
      outputWS->setBinEdges(workspaceIndex, std::move(timeBins));

      pivot++; // one-off difference between x and y

      // fix the counts using the pivot point
      auto &yIn = m_inputWS->y(workspaceIndex);
      auto &yOut = outputWS->mutableY(workspaceIndex);

      auto lengthFirstPartY = std::distance(yIn.begin() + pivot, yIn.end());
      std::copy(yIn.begin() + pivot, yIn.end(), yOut.begin());
      std::copy(yIn.begin(), yIn.begin() + pivot,
                yOut.begin() + lengthFirstPartY);

      // fix the uncertainties using the pivot point
      auto &eIn = m_inputWS->e(workspaceIndex);
      auto &eOut = outputWS->mutableE(workspaceIndex);

      auto lengthFirstPartE = std::distance(eIn.begin() + pivot, eIn.end());
      std::copy(eIn.begin() + pivot, eIn.end(), eOut.begin());
      std::copy(eIn.begin(), eIn.begin() + pivot,
                eOut.begin() + lengthFirstPartE);
    }
    m_progress->report();
    PARALLEL_END_INTERUPT_REGION
  }
  PARALLEL_CHECK_INTERUPT_REGION

  m_inputWS.reset();
  this->runMaskDetectors();
}

void UnwrapSNS::execEvent() {
  // set up the output workspace
  MatrixWorkspace_sptr matrixOutW = this->getProperty("OutputWorkspace");
  if (matrixOutW != m_inputWS) {
    matrixOutW = m_inputWS->clone();
    setProperty("OutputWorkspace", matrixOutW);
  }
  auto outW = std::dynamic_pointer_cast<EventWorkspace>(matrixOutW);

  // set up the progress bar
  m_progress =
      std::make_unique<Progress>(this, 0.0, 1.0, m_numberOfSpectra * 2);

  // algorithm assumes the data is sorted so it can jump out early
  outW->sortAll(Mantid::DataObjects::TOF_SORT, m_progress.get());

  this->getTofRangeData(true);

  // without the primary flight path the algorithm cannot work
  const auto &spectrumInfo = m_inputWS->spectrumInfo();
  const double L1 = spectrumInfo.l1();

  // do the actual work
  for (int workspaceIndex = 0; workspaceIndex < m_numberOfSpectra;
       workspaceIndex++) {
    std::size_t numEvents = outW->getSpectrum(workspaceIndex).getNumberEvents();
    double Ld = -1.0;
    if (spectrumInfo.hasDetectors(workspaceIndex))
      Ld = L1 + spectrumInfo.l2(workspaceIndex);

    std::vector<double> time_bins;
    if (outW->x(0).size() > 2) {
      this->unwrapX(m_inputWS->x(workspaceIndex), time_bins, Ld);
      outW->setBinEdges(workspaceIndex, std::move(time_bins));
    } else {
      outW->setSharedX(workspaceIndex, m_inputWS->sharedX(workspaceIndex));
    }
    if (numEvents > 0) {
      std::vector<double> times(numEvents);
      outW->getSpectrum(workspaceIndex).getTofs(times);
      double filterVal = m_Tmin * Ld / m_LRef;
      for (size_t j = 0; j < numEvents; j++) {
        if (times[j] < filterVal)
          times[j] += m_frameWidth;
        else
          break; // stop filtering
      }
      outW->getSpectrum(workspaceIndex).setTofs(times);
    }
    m_progress->report();
  }

  outW->clearMRU();
  this->runMaskDetectors();
}

int UnwrapSNS::unwrapX(const Mantid::HistogramData::HistogramX &datain,
                       std::vector<double> &dataout, const double &Ld) {
  std::vector<double> tempX_L; // lower half - to be frame wrapped
  tempX_L.reserve(m_XSize);
  tempX_L.clear();
  std::vector<double> tempX_U; // upper half - to not be frame wrapped
  tempX_U.reserve(m_XSize);
  tempX_U.clear();

  double filterVal = m_Tmin * Ld / m_LRef;
  dataout.clear();
  int specialBin = 0;
  for (int bin = 0; bin < m_XSize; ++bin) {
    // This is the time-of-flight value under consideration in the current
    // iteration of the loop
    const double tof = datain[bin];
    if (tof < filterVal) {
      tempX_L.emplace_back(tof + m_frameWidth);
      // Record the bins that fall in this range for copying over the data &
      // errors
      if (specialBin < bin)
        specialBin = bin;
    } else {
      tempX_U.emplace_back(tof);
    }
  } // loop over X values

  // now put it back into the vector supplied
  dataout.clear();
  dataout.insert(dataout.begin(), tempX_U.begin(), tempX_U.end());
  dataout.insert(dataout.end(), tempX_L.begin(), tempX_L.end());
  assert(datain.size() == dataout.size());

  return specialBin;
}

void UnwrapSNS::getTofRangeData(const bool isEvent) {
  // get the Tmin/Tmax properties
  m_Tmin = this->getProperty("Tmin");
  m_Tmax = this->getProperty("Tmax");

  // if either the values are not specified by properties, find them from the
  // data
  double empty = Mantid::EMPTY_DBL();
  if ((m_Tmin == empty) || (m_Tmax == empty)) {
    // get data min/max values
    double dataTmin;
    double dataTmax;
    if (isEvent) {
      m_inputEvWS->sortAll(DataObjects::TOF_SORT, nullptr);
      m_inputEvWS->getEventXMinMax(dataTmin, dataTmax);
    } else {
      m_inputWS->getXMinMax(dataTmin, dataTmax);
    }

    // fix the unspecified values
    if (m_Tmin == empty) {
      m_Tmin = dataTmin;
    }
    if (m_Tmax == empty) {
      m_Tmax = dataTmax;
    }
  }

  // check the frame width
  m_frameWidth = m_Tmax - m_Tmin;

  g_log.information() << "Frame range in microseconds is: " << m_Tmin << " - "
                      << m_Tmax << "\n";
  if (m_Tmin < 0.)
    throw std::runtime_error("Cannot have Tmin less than zero");
  if (m_Tmin > m_Tmax)
    throw std::runtime_error("Have case of Tmin > Tmax");

  g_log.information() << "Wavelength cuttoff is : "
                      << (m_conversionConstant * m_Tmin / m_LRef)
                      << "Angstrom, Frame width is: " << m_frameWidth
                      << "microseconds\n";
}

void UnwrapSNS::runMaskDetectors() {
  IAlgorithm_sptr alg = createChildAlgorithm("MaskDetectors");
  alg->setProperty<MatrixWorkspace_sptr>("Workspace",
                                         this->getProperty("OutputWorkspace"));
  alg->setProperty<MatrixWorkspace_sptr>("MaskedWorkspace",
                                         this->getProperty("InputWorkspace"));
  if (!alg->execute())
    throw std::runtime_error(
        "MaskDetectors Child Algorithm has not executed successfully");
}

} // namespace Algorithms
} // namespace Mantid