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]


// Boost.Geometry (aka GGL, Generic Geometry Library)
// Unit Test

// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
// Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
// Copyright (c) 2009-2012 Mateusz Loskot, London, UK.

// This file was modified by Oracle on 2014, 2015, 2016, 2017.
// Modifications copyright (c) 2014-2017 Oracle and/or its affiliates.

// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle

// Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
// (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.

// Use, modification and distribution is subject to the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)


#include <geometry_test_common.hpp>

#include <boost/concept_check.hpp>

#include <boost/geometry/algorithms/assign.hpp>
#include <boost/geometry/algorithms/distance.hpp>
#include <boost/geometry/formulas/vincenty_inverse.hpp>
#include <boost/geometry/formulas/vincenty_direct.hpp>
#include <boost/geometry/geometries/point.hpp>
#include <boost/geometry/srs/spheroid.hpp>
#include <boost/geometry/strategies/concepts/distance_concept.hpp>
#include <boost/geometry/strategies/geographic/distance_vincenty.hpp>
#include <boost/geometry/strategies/geographic/side_vincenty.hpp>

#include <test_common/test_point.hpp>

#ifdef HAVE_TTMATH
#  include <boost/geometry/extensions/contrib/ttmath_stub.hpp>
#endif

template <typename T>
void normalize_deg(T & deg)
{
    while ( deg > T(180) )
        deg -= T(360);
    while ( deg <= T(-180) )
        deg += T(360);
}

template <typename T>
T difference_deg(T const& a1, T const& a2)
{
    T d = a1 - a2;
    normalize_deg(d);
    return d;
}

template <typename T>
void check_deg(std::string const& name, T const& a1, T const& a2, T const& percent, T const& error)
{
    T diff = bg::math::abs(difference_deg(a1, a2));
    
    if ( bg::math::equals(a1, T(0)) || bg::math::equals(a2, T(0)) )
    {
        if ( diff > error )
        {
            BOOST_ERROR(name << " - the difference {" << diff << "} between {" << a1 << "} and {" << a2 << "} exceeds {" << error << "}");
        }
    }
    else
    {
        T greater = (std::max)(bg::math::abs(a1), bg::math::abs(a2));

        if ( diff > greater * percent / T(100) )
        {
            BOOST_ERROR(name << " the difference {" << diff << "} between {" << a1 << "} and {" << a2 << "} exceeds {" << percent << "}%");
        }
    }
}

double azimuth(double deg, double min, double sec)
{
    min = fabs(min);
    sec = fabs(sec);

    if ( deg < 0 )
    {
        min = -min;
        sec = -sec;
    }

    return deg + min/60.0 + sec/3600.0;
}

double azimuth(double deg, double min)
{
    return azimuth(deg, min, 0.0);
}

template <typename P>
bool non_precise_ct()
{
    typedef typename bg::coordinate_type<P>::type ct;
    return boost::is_integral<ct>::value || boost::is_float<ct>::value;
}

template <typename P1, typename P2, typename Spheroid>
void test_vincenty(double lon1, double lat1, double lon2, double lat2,
                   double expected_distance,
                   double expected_azimuth_12,
                   double /*expected_azimuth_21*/,
                   Spheroid const& spheroid)
{
    typedef typename bg::promote_floating_point
        <
            typename bg::select_calculation_type<P1, P2, void>::type
        >::type calc_t;

    calc_t tolerance = non_precise_ct<P1>() || non_precise_ct<P2>() ?
                       5.0 : 0.001;
    calc_t error = non_precise_ct<P1>() || non_precise_ct<P2>() ?
                   1e-5 : 1e-12;

    // formula
    {
        double const d2r = bg::math::d2r<double>();
        double const r2d = bg::math::r2d<double>();

        typedef bg::formula::vincenty_inverse<calc_t, true, true> inverse_formula;
        typename inverse_formula::result_type
            result_i = inverse_formula::apply(lon1 * d2r,
                                             lat1 * d2r,
                                             lon2 * d2r,
                                             lat2 * d2r,
                                             spheroid);
        calc_t dist = result_i.distance;
        calc_t az12 = result_i.azimuth;
        //calc_t az21 = vi.azimuth21();

        calc_t az12_deg = az12 * r2d;
        //calc_t az21_deg = az21 * r2d;
        
        BOOST_CHECK_CLOSE(dist, calc_t(expected_distance), tolerance);
        check_deg("az12_deg", az12_deg, calc_t(expected_azimuth_12), tolerance, error);
        //check_deg("az21_deg", az21_deg, calc_t(expected_azimuth_21), tolerance, error);

        typedef bg::formula::vincenty_direct<calc_t> direct_formula;
        typename direct_formula::result_type
            result_d = direct_formula::apply(lon1 * d2r,
                                             lat1 * d2r,
                                             dist,
                                             az12,
                                             spheroid);
        calc_t direct_lon2 = result_d.lon2;
        calc_t direct_lat2 = result_d.lat2;
        //calc_t direct_az21 = vd.azimuth21();

        calc_t direct_lon2_deg = direct_lon2 * r2d;
        calc_t direct_lat2_deg = direct_lat2 * r2d;
        //calc_t direct_az21_deg = direct_az21 * r2d;
        
        check_deg("direct_lon2_deg", direct_lon2_deg, calc_t(lon2), tolerance, error);
        check_deg("direct_lat2_deg", direct_lat2_deg, calc_t(lat2), tolerance, error);
        //check_deg("direct_az21_deg", direct_az21_deg, az21_deg, tolerance, error);
    }

    // distance strategies
    {
        typedef bg::strategy::distance::vincenty<Spheroid> vincenty_type;
        typedef bg::strategy::distance::geographic<bg::strategy::vincenty, Spheroid> geographic_type;

        BOOST_CONCEPT_ASSERT(
            (
                bg::concepts::PointDistanceStrategy<vincenty_type, P1, P2>)
            );

        vincenty_type vincenty(spheroid);
        geographic_type geographic(spheroid);
        typedef typename bg::strategy::distance::services::return_type<vincenty_type, P1, P2>::type return_type;

        P1 p1;
        P2 p2;

        bg::assign_values(p1, lon1, lat1);
        bg::assign_values(p2, lon2, lat2);
        
        BOOST_CHECK_CLOSE(vincenty.apply(p1, p2), return_type(expected_distance), tolerance);
        BOOST_CHECK_CLOSE(geographic.apply(p1, p2), return_type(expected_distance), tolerance);
        BOOST_CHECK_CLOSE(bg::distance(p1, p2, vincenty), return_type(expected_distance), tolerance);
    }
}

template <typename P1, typename P2>
void test_vincenty(double lon1, double lat1, double lon2, double lat2,
                   double expected_distance,
                   double expected_azimuth_12,
                   double expected_azimuth_21)
{
    test_vincenty<P1, P2>(lon1, lat1, lon2, lat2,
                          expected_distance, expected_azimuth_12, expected_azimuth_21,
                          bg::srs::spheroid<double>());
}

template <typename PS, typename P>
void test_side(double lon1, double lat1,
               double lon2, double lat2,
               double lon, double lat,
               int expected_side)
{
    // Set radius type, but for integer coordinates we want to have floating point radius type
    typedef typename bg::promote_floating_point
        <
            typename bg::coordinate_type<PS>::type
        >::type rtype;

    typedef bg::srs::spheroid<rtype> stype;

    typedef bg::strategy::side::vincenty<stype> strategy_type;
    typedef bg::strategy::side::geographic<bg::strategy::vincenty, stype> strategy2_type;

    strategy_type strategy;
    strategy2_type strategy2;

    PS p1, p2;
    P p;

    bg::assign_values(p1, lon1, lat1);
    bg::assign_values(p2, lon2, lat2);
    bg::assign_values(p, lon, lat);

    int side = strategy.apply(p1, p2, p);
    int side2 = strategy2.apply(p1, p2, p);

    BOOST_CHECK_EQUAL(side, expected_side);
    BOOST_CHECK_EQUAL(side2, expected_side);
}

template <typename P1, typename P2>
void test_all()
{
    // See:
    //  - http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp
    //  - http://www.ga.gov.au/geodesy/datums/vincenty_direct.jsp
    // Values in the comments below was calculated using the above pages
    // in some cases distances may be different, previously used values was left

    // use km
    double gda_a = 6378.1370;
    double gda_f = 1.0 / 298.25722210;
    double gda_b = gda_a * ( 1.0 - gda_f );
    bg::srs::spheroid<double> gda_spheroid(gda_a, gda_b);

    // Test fractional coordinates only for non-integral types
    if ( BOOST_GEOMETRY_CONDITION(
            ! boost::is_integral<typename bg::coordinate_type<P1>::type>::value
         && ! boost::is_integral<typename bg::coordinate_type<P2>::type>::value  ) )
    {
        // Flinders Peak -> Buninyong
        test_vincenty<P1, P2>(azimuth(144,25,29.52440), azimuth(-37,57,3.72030),
                              azimuth(143,55,35.38390), azimuth(-37,39,10.15610),
                              54.972271, azimuth(306,52,5.37), azimuth(127,10,25.07),
                              gda_spheroid);
    }

    // Lodz -> Trondheim
    test_vincenty<P1, P2>(azimuth(19,28), azimuth(51,47),
                          azimuth(10,21), azimuth(63,23),
                          1399.032724, azimuth(340,54,25.14), azimuth(153,10,0.19),
                          gda_spheroid);
    // London -> New York
    test_vincenty<P1, P2>(azimuth(0,7,39), azimuth(51,30,26),
                          azimuth(-74,0,21), azimuth(40,42,46),
                          5602.044851, azimuth(288,31,36.82), azimuth(51,10,33.43),
                          gda_spheroid);

    // Shanghai -> San Francisco
    test_vincenty<P1, P2>(azimuth(121,30), azimuth(31,12),
                          azimuth(-122,25), azimuth(37,47),
                          9899.698550, azimuth(45,12,44.76), azimuth(309,50,20.88),
                          gda_spheroid);

    test_vincenty<P1, P2>(0, 0, 0, 50, 5540.847042, 0, 180, gda_spheroid); // N
    test_vincenty<P1, P2>(0, 0, 0, -50, 5540.847042, 180, 0, gda_spheroid); // S
    test_vincenty<P1, P2>(0, 0, 50, 0, 5565.974540, 90, -90, gda_spheroid); // E
    test_vincenty<P1, P2>(0, 0, -50, 0, 5565.974540, -90, 90, gda_spheroid); // W
    
    test_vincenty<P1, P2>(0, 0, 50, 50, 7284.879297, azimuth(32,51,55.87), azimuth(237,24,50.12), gda_spheroid); // NE
    
    // The original distance values, azimuths calculated using the web form mentioned above
    // Using default spheroid units (meters)
    test_vincenty<P1, P2>(0, 89, 1, 80, 1005153.5769, azimuth(178,53,23.85), azimuth(359,53,18.35)); // sub-polar
    test_vincenty<P1, P2>(4, 52, 4, 52, 0.0, 0, 0); // no point difference
    test_vincenty<P1, P2>(4, 52, 3, 40, 1336039.890, azimuth(183,41,29.08), azimuth(2,58,5.13)); // normal case

    test_side<P1, P2>(0, 0, 0, 1, 0, 2, 0);
    test_side<P1, P2>(0, 0, 0, 1, 0, -2, 0);
    test_side<P1, P2>(10, 0, 10, 1, 10, 2, 0);
    test_side<P1, P2>(10, 0, 10, -1, 10, 2, 0);

    test_side<P1, P2>(10, 0, 10, 1, 0, 2, 1); // left
    test_side<P1, P2>(10, 0, 10, -1, 0, 2, -1); // right

    test_side<P1, P2>(-10, -10, 10, 10, 10, 0, -1); // right
    test_side<P1, P2>(-10, -10, 10, 10, -10, 0, 1); // left
    test_side<P1, P2>(170, -10, -170, 10, -170, 0, -1); // right
    test_side<P1, P2>(170, -10, -170, 10, 170, 0, 1); // left
}

template <typename P>
void test_all()
{
    test_all<P, P>();
}

int test_main(int, char* [])
{
    //test_all<float[2]>();
    //test_all<double[2]>();
    test_all<bg::model::point<double, 2, bg::cs::geographic<bg::degree> > >();
    test_all<bg::model::point<float, 2, bg::cs::geographic<bg::degree> > >();
    test_all<bg::model::point<int, 2, bg::cs::geographic<bg::degree> > >();

#if defined(HAVE_TTMATH)
    test_all<bg::model::point<ttmath::Big<1,4>, 2, bg::cs::geographic<bg::degree> > >();
    test_all<bg::model::point<ttmath_big, 2, bg::cs::geographic<bg::degree> > >();
#endif


    return 0;
}