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]


\defgroup Unuran Unuran

\brief Universal Non Uniform Random number generator for generating non uniform pseudo-random numbers.

\ingroup Math

UNU.RAN, (Universal Non Uniform Random number generator for generating non uniform pseudo-random numbers)
is an ANSI C library licensed under GPL.<br>
It contains universal (also called automatic or black-box) algorithms that can generate random numbers from
large classes of continuous or discrete distributions, and also from practically all standard distributions.
An extensive online documentation are available at the (UNU.RAN Web Site)[http://statistik.wu-wien.ac.at/unuran/]

New classes have been introduced to use the UNU.RAN C library from ROOT and C++ from ROOT and using C++ objects.
To use UNU.RAN one needs always an instance of the class **TUnuran**.
It can then be used in two distinct ways:
- using the UNU.RAN native string API for pre-defined distributions (see<a href="http://statistik.wu-wien.ac.at/unuran/doc/unuran.html#StringAPI"> UNU.RAN documentation</a> for the string API):

~~~{.cpp}
          TUnuran unr;
          //initialize unuran to generate normal random numbers using a "arou" method
          unr.Init("normal()","method=arou");
          //......
          // sample distributions N times (generate N random numbers)
          for (int i = 0; i &lt; N; ++i)
                double x = unr.Sample();

~~~


- Using a distribution object. We have then the following cases depending on the dimension and the distribution object.

- For 1D distribution the class **TUnuranContDist** must be used.
    - A **TUnuranContDist** object can be created from a function
    providing the pdf (probability density function) and optionally one providing the derivative of the pdf.
   - If the derivative is not provided and the generation method requires it, then it is estimated numerically.
    - The user can optionally provide the
     - cdf (cumulative distribution function) via the **TUnuranContDist::SetCdf** function,
     - the mode via **TUnuranContDist::SetMode**,
     - the domain via **TUnuranContDist::SetDomain** for generating numbers in a restricted region,
     - the area below the pdf via **TUnuranContDist::SetPdfArea**.

Some of this information is required depending on the chosen UNURAN generation method.

~~~~{.cpp}
       //1D case: create a distribution from two TF1 object pointers pdfFunc
       TUnuranContDist  dist( pdfFunc);
       //initialize unuran passing the distribution and a string defining the method
       unr.Init(dist, "method=hinv");
       // sample distribution  N times (generate N random numbers)
       for (int i = 0; i &lt; N; ++i)
          double x = unr.Sample();
~~~~

- For multi-dimensional distribution the class **TUnuranMultiContDist** must be used.
In this case only the multi-dimensional pdf is required

~~~~{.cpp}
      //Multi-Dim case from a TF1 (or TF2 or TF3) object describing a multi-dimensional function
      TUnuranMultiContDist  dist( pdfFuncMulti);
      // the recommended method for multi-dimensional function is "hitro"
      unr.Init(dist, "method=hitro");
      // sample distribution  N times (generate N random numbers)
      double x[NDIM];
      for (int i = 0; i &lt; N; ++i)
      unr.SampleMulti(x);
~~~~

- For discrete distribution the class **TUnuranDiscrDist** must be used.
   The distribution can be initialized from a TF1 or from a vector of probabilities.

~~~~{.cpp}
      // create distribution from a vector of probabilities
         double pv[NSize] = {0.1,0.2,.......};
      TUnuranDiscrDist  dist(pv, pv+NSize);
      // the recommended method for discrete distribution is
      unr.Init(dist, "method=dgt");
      // sample N times (generate N random numbers)
      for (int i = 0; i &lt; N; ++i)
         int k = unr.SampleDiscr();
~~~~

- For empirical distribution the class **TUnuranEmpDist** must be used.
  In this case one can generate random numbers from a set of data (un-binned)  in one or multi-dimension or
  from a set of binned data in one dimension (similar to TH1::GetRandom() ).
  - For unbin data the parent distribution is estimated by UNU.RAN using a gaussian kernel smoothing algorithm.
   One can create the distribution class directly from a vector of data or from the buffer of TH1.

~~~~{.cpp}
      // create distribution from a set of data 1D
      // vdata is an std::vector containing the data
      TUnuranEmpDist  dist( vdata.begin(),vdata.end());
      unr.Init(dist);
         // sample N times (generate N random numbers)
      for (int i = 0; i &lt; N; ++i)
         double x = unr.Sample();
~~~~

- In the case of multi-dimension emprical distributions one needs to pass in addition to the iterators, the data dimension. It is assumed that the data are stored in the vector in this order : `(x0,y0,...),(x1,y1,....)`.

- For binned data (only one dimensional data are supported) one uses directly the histogram

~~~{.cpp}
      // create an empirical distribution from an histogram
      // if the histogram has a buffer one must use TUnuranEmpDist(h1,false)
      TH1 * h1 = ... // histogram pointer
      TUnuranEmpDist  binDist( h1);
      unr.Init(binDist);
         // sample N times (generate N random numbers)
      for (int i = 0; i &lt; N; ++i)
         double x = unr.Sample();
~~~

- This is equivalent to TH1::GetRandom(), but sampling is faster, therefore, since it requires some initialization time,
  it becomes convenient when generating a large sample of random numbers.

Functionality is also provided via the C++ classes for using a different random number generator by passing a
TRandom pointer when constructing the TUnuran class (by default the ROOT gRandom is passed to UNURAN).

The (UNU.RAN documentation)[http://statistik.wu-wien.ac.at/unuran/doc/unuran.html#Top] provides a detailed
description of all the available methods and the possible options which one can pass to UNU.RAN for the various distributions.