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) 2012-2020 The plumed team
   (see the PEOPLE file at the root of the distribution for a list of names)

   See http://www.plumed.org for more information.

   This file is part of plumed, version 2.

   plumed is free software: you can redistribute it and/or modify
   it under the terms of the GNU Lesser General Public License as published by
   the Free Software Foundation, either version 3 of the License, or
   (at your option) any later version.

   plumed is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public License
   along with plumed.  If not, see <http://www.gnu.org/licenses/>.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
#include "PathMSDBase.h"
#include "core/PlumedMain.h"

using namespace std;

namespace PLMD {
namespace colvar {

//+PLUMEDOC COLVAR PROPERTYMAP
/*
Calculate generic property maps.

This Colvar calculates the property maps according to the work of Spiwok \cite Spiwok:2011ce.


Basically it calculates
\f{eqnarray*}{
X=\frac{\sum_i X_i*\exp(-\lambda D_i(x))}{\sum_i  \exp(-\lambda D_i(x))} \\
Y=\frac{\sum_i Y_i*\exp(-\lambda D_i(x))}{\sum_i  \exp(-\lambda D_i(x))} \\
\cdots\\
zzz=-\frac{1}{\lambda}\log(\sum_i  \exp(-\lambda D_i(x)))
\f}

where the parameters \f$X_i\f$  and  \f$Y_i\f$ are provided in the input pdb (allv.pdb in this case) and
 \f$D_i(x)\f$  is the mean squared displacement after optimal alignment calculated on the pdb frames you input (see Kearsley).


When running with periodic boundary conditions, the atoms should be
in the proper periodic image. This is done automatically since PLUMED 2.5,
by considering the ordered list of atoms and rebuilding molecules using a procedure
that is equivalent to that done in \ref WHOLEMOLECULES . Notice that
rebuilding is local to this action. This is different from \ref WHOLEMOLECULES
which actually modifies the coordinates stored in PLUMED.

In case you want to recover the old behavior you should use the NOPBC flag.
In that case you need to take care that atoms are in the correct
periodic image.

\par Examples

\plumedfile
p3: PROPERTYMAP REFERENCE=allv.pdb PROPERTY=X,Y LAMBDA=69087 NEIGH_SIZE=8 NEIGH_STRIDE=4
PRINT ARG=p3.X,p3.Y,p3.zzz STRIDE=1 FILE=colvar FMT=%8.4f
\endplumedfile

note that NEIGH_STRIDE=4 NEIGH_SIZE=8 control the neighbor list parameter (optional but
recommended for performance) and states that the neighbor list will be calculated every 4
steps and consider only the closest 8 member to the actual md snapshots.

In this case the input line instructs plumed to look for two properties X and Y with attached values in the REMARK
line of the reference pdb (Note: No spaces from X and = and 1 !!!!).
e.g.

\auxfile{allv.pdb}
REMARK X=1 Y=2
ATOM      1  CL  ALA     1      -3.171   0.295   2.045  1.00  1.00
ATOM      5  CLP ALA     1      -1.819  -0.143   1.679  1.00  1.00
END
REMARK X=2 Y=3
ATOM      1  CL  ALA     1      -3.175   0.365   2.024  1.00  1.00
ATOM      5  CLP ALA     1      -1.814  -0.106   1.685  1.00  1.00
END
\endauxfile

\note
The implementation of this collective variable and of \ref PATHMSD
is shared, as well as most input options.

*/
//+ENDPLUMEDOC

class PropertyMap : public PathMSDBase {
public:
  explicit PropertyMap(const ActionOptions&);
  static void registerKeywords(Keywords& keys);
};

PLUMED_REGISTER_ACTION(PropertyMap,"PROPERTYMAP")

void PropertyMap::registerKeywords(Keywords& keys) {
  PathMSDBase::registerKeywords(keys);
  keys.add("compulsory","PROPERTY","the property to be used in the indexing: this goes in the REMARK field of the reference");
  ActionWithValue::useCustomisableComponents(keys);
  keys.addOutputComponent("zzz","default","the minimum distance from the reference points");
}

PropertyMap::PropertyMap(const ActionOptions&ao):
  Action(ao),
  PathMSDBase(ao)
{
  // this is the only additional keyword needed
  parseVector("PROPERTY",labels);
  checkRead();
  log<<"  Bibliography "
     <<plumed.cite("Spiwok V, Kralova B  J. Chem. Phys. 135,  224504 (2011)")
     <<"\n";
  if(labels.size()==0) {
    char buf[500];
    sprintf(buf,"Need to specify PROPERTY with this action\n");
    plumed_merror(buf);
  } else {
    for(unsigned i=0; i<labels.size(); i++) {
      log<<" found custom propety to be found in the REMARK line: "<<labels[i].c_str()<<"\n";
      addComponentWithDerivatives(labels[i]); componentIsNotPeriodic(labels[i]);
    }
    // add distance anyhow
    addComponentWithDerivatives("zzz"); componentIsNotPeriodic("zzz");
    //reparse the REMARK field and pick the index
    for(unsigned i=0; i<pdbv.size(); i++) {
      // now look for X=1.34555 Y=5.6677
      vector<double> labelvals;
      for(unsigned j=0; j<labels.size(); j++) {
        double val;
        if( pdbv[i].getArgumentValue(labels[j],val) ) {labelvals.push_back(val);}
        else {
          char buf[500];
          sprintf(buf,"PROPERTY LABEL \" %s \" NOT FOUND IN REMARK FOR FRAME %u \n",labels[j].c_str(),i);
          plumed_merror(buf);
        };
      }
      indexvec.push_back(labelvals);
    }
  }
  requestAtoms(pdbv[0].getAtomNumbers());

}

}
}