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]


"""
========
Max-tree
========

The max-tree is a hierarchical representation of an image that is the basis
for a large family of morphological filters.

If we apply a threshold operation to an image, we obtain a binary image
containing one or several connected components. If we apply a lower
threshold, all the connected components from the higher threshold are
contained in the connected components from the lower threshold. This
naturally defines a hierarchy of nested components that can be
represented by a tree. whenever a connected component A obtained by
thresholding with threshold t1 is contained in a component B obtained by
thresholding with threshold t1 < t2, we say that B is the parent of A.
The resulting tree structure is called a component tree. The max-tree
is a compact representation of such a component tree. [1]_, [2]_, [3]_, [4]_

In this example we give an intuition of what a max-tree is.

References
----------
.. [1] Salembier, P., Oliveras, A., & Garrido, L. (1998). Antiextensive
       Connected Operators for Image and Sequence Processing.
       IEEE Transactions on Image Processing, 7(4), 555-570.
       :DOI:`10.1109/83.663500`
.. [2] Berger, C., Geraud, T., Levillain, R., Widynski, N., Baillard, A.,
       Bertin, E. (2007). Effective Component Tree Computation with
       Application to Pattern Recognition in Astronomical Imaging.
       In International Conference on Image Processing (ICIP) (pp. 41-44).
       :DOI:`10.1109/ICIP.2007.4379949`
.. [3] Najman, L., & Couprie, M. (2006). Building the component tree in
       quasi-linear time. IEEE Transactions on Image Processing, 15(11),
       3531-3539.
       :DOI:`10.1109/TIP.2006.877518`
.. [4] Carlinet, E., & Geraud, T. (2014). A Comparative Review of
       Component Tree Computation Algorithms. IEEE Transactions on Image
       Processing, 23(9), 3885-3895.
       :DOI:`10.1109/TIP.2014.2336551`
"""

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from skimage.morphology import max_tree
import networkx as nx


#####################################################################
# Before we start : a few helper functions

def plot_img(ax, image, title, plot_text, image_values):
    """Plot an image, overlaying image values or indices."""
    ax.imshow(image, cmap='gray', aspect='equal', vmin=0, vmax=np.max(image))
    ax.set_title(title)
    ax.set_yticks([])
    ax.set_xticks([])

    for x in np.arange(-0.5, image.shape[0], 1.0):
        ax.add_artist(Line2D((x, x), (-0.5, image.shape[0] - 0.5),
                             color='blue', linewidth=2))

    for y in np.arange(-0.5, image.shape[1], 1.0):
        ax.add_artist(Line2D((-0.5, image.shape[1]), (y, y),
                             color='blue', linewidth=2))

    if plot_text:
        for i, j in np.ndindex(*image_values.shape):
            ax.text(j, i, image_values[i, j], fontsize=8,
                    horizontalalignment='center',
                    verticalalignment='center',
                    color='red')
    return


def prune(G, node, res):
    """Transform a canonical max tree to a max tree."""
    value = G.nodes[node]['value']
    res[node] = str(node)
    preds = [p for p in G.predecessors(node)]
    for p in preds:
        if (G.nodes[p]['value'] == value):
            res[node] += ', %i' % p
            G.remove_node(p)
        else:
            prune(G, p, res)
    G.nodes[node]['label'] = res[node]
    return


def accumulate(G, node, res):
    """Transform a max tree to a component tree."""
    total = G.nodes[node]['label']
    parents = G.predecessors(node)
    for p in parents:
        total += ', ' + accumulate(G, p, res)
    res[node] = total
    return total


def position_nodes_for_max_tree(G, image_rav, root_x=4, delta_x=1.2):
    """Set the position of nodes of a max-tree.

    This function helps to visually distinguish between nodes at the same
    level of the hierarchy and nodes at different levels.
    """
    pos = {}
    for node in reversed(list(nx.topological_sort(canonical_max_tree))):
        value = G.nodes[node]['value']
        if canonical_max_tree.out_degree(node) == 0:
            # root
            pos[node] = (root_x, value)

        in_nodes = [y for y in canonical_max_tree.predecessors(node)]

        # place the nodes at the same level
        level_nodes = [y for y in
                       filter(lambda x: image_rav[x] == value, in_nodes)]
        nb_level_nodes = len(level_nodes) + 1

        c = nb_level_nodes // 2
        i = - c
        if (len(level_nodes) < 3):
            hy = 0
            m = 0
        else:
            hy = 0.25
            m = hy / (c - 1)

        for level_node in level_nodes:
            if(i == 0):
                i += 1
            if (len(level_nodes) < 3):
                pos[level_node] = (pos[node][0] + i * 0.6 * delta_x, value)
            else:
                pos[level_node] = (pos[node][0] + i * 0.6 * delta_x,
                                   value + m * (2 * np.abs(i) - c - 1))
            i += 1

        # place the nodes at different levels
        other_level_nodes = [y for y in
                             filter(lambda x: image_rav[x] > value, in_nodes)]
        if (len(other_level_nodes) == 1):
            i = 0
        else:
            i = - len(other_level_nodes) // 2
        for other_level_node in other_level_nodes:
            if((len(other_level_nodes) % 2 == 0) and (i == 0)):
                i += 1
            pos[other_level_node] = (pos[node][0] + i * delta_x,
                                     image_rav[other_level_node])
            i += 1

    return pos


def plot_tree(graph, positions, ax, *, title='', labels=None,
              font_size=8, text_size=8):
    """Plot max and component trees."""
    nx.draw_networkx(graph, pos=positions, ax=ax,
                     node_size=40, node_shape='s', node_color='white',
                     font_size=font_size, labels=labels)
    xlimit = ax.get_xlim()
    for v in range(image_rav.min(), image_rav.max() + 1):
        ax.hlines(v - 0.5, -3, 10, linestyles='dotted')
        ax.text(-3, v - 0.15, "val: %i" % v, fontsize=text_size)
    ax.hlines(v + 0.5, -3, 10, linestyles='dotted')
    ax.set_xlim(-3, 10)
    ax.set_title(title)
    ax.set_axis_off()


#####################################################################
# Image Definition
# ================
# We define a small test image.
# For clarity, we choose an example image, where image values cannot be
# confounded with indices (different range).
image = np.array([[40, 40, 39, 39, 38],
                  [40, 41, 39, 39, 39],
                  [30, 30, 30, 32, 32],
                  [33, 33, 30, 32, 35],
                  [30, 30, 30, 33, 36]], dtype=np.uint8)


#####################################################################
# Max-tree
# ========
# Next, we calculate the max-tree of this image.
# max-tree of the image
P, S = max_tree(image)

P_rav = P.ravel()


#####################################################################
# Image plots
# ===========
# Then, we visualize the image and its raveled indices.
# Concretely, we plot the image with the following overlays:
# - the image values
# - the raveled indices (serve as pixel identifiers)
# - the output of the max_tree function

# raveled image
image_rav = image.ravel()

# raveled indices of the example image (for display purpose)
raveled_indices = np.arange(image.size).reshape(image.shape)

fig, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True, figsize=(9, 3))

plot_img(ax1, image - image.min(), 'Image Values',
         plot_text=True, image_values=image)
plot_img(ax2, image - image.min(), 'Raveled Indices',
         plot_text=True, image_values=raveled_indices)
plot_img(ax3, image - image.min(), 'Max-tree indices',
         plot_text=True, image_values=P)


#####################################################################
# Visualizing threshold operations
# ================================
# Now, we investigate the results of a series of threshold operations.
# The component tree (and max-tree) provide representations of the
# inclusion relationships between connected components at different
# levels.
fig, axes = plt.subplots(3, 3, sharey=True, sharex=True, figsize=(6, 6))
thresholds = np.unique(image)
for k, threshold in enumerate(thresholds):
    bin_img = image >= threshold
    plot_img(axes[(k // 3), (k % 3)], bin_img, 'Threshold : %i' % threshold,
             plot_text=True, image_values=raveled_indices)


#####################################################################
# Max-tree plots
# ==============
# Now, we plot the component and max-trees. A component tree relates
# the different pixel sets resulting from all possible threshold operations
# to each other. There is an arrow in the graph, if a component at one level
# is included in the component of a lower level. The max-tree is just
# a different encoding of the pixel sets.
#
# 1. the component tree: pixel sets are explicitly written out. We see for
#    instance that {6} (result of applying a threshold at 41) is the parent
#    of {0, 1, 5, 6} (threshold at 40).
# 2. the max-tree: only pixels that come into the set at this level
#    are explicitly written out. We therefore will write
#    {6} -> {0,1,5} instead of {6} -> {0, 1, 5, 6}
# 3. the canonical max-treeL this is the representation which is given by
#    our implementation. Here, every pixel is a node. Connected components
#    of several pixels are represented by one of the pixels. We thus replace
#    {6} -> {0,1,5} by {6} -> {5}, {1} -> {5}, {0} -> {5}
#    This allows us to represent the graph by an image (top row, third column).

# the canonical max-tree graph
canonical_max_tree = nx.DiGraph()
canonical_max_tree.add_nodes_from(S)
for node in canonical_max_tree.nodes():
    canonical_max_tree.nodes[node]['value'] = image_rav[node]
canonical_max_tree.add_edges_from([(n, P_rav[n]) for n in S[1:]])

# max-tree from the canonical max-tree
nx_max_tree = nx.DiGraph(canonical_max_tree)
labels = {}
prune(nx_max_tree, S[0], labels)

# component tree from the max-tree
labels_ct = {}
total = accumulate(nx_max_tree, S[0], labels_ct)

# positions of nodes : canonical max-tree (CMT)
pos_cmt = position_nodes_for_max_tree(canonical_max_tree, image_rav)

# positions of nodes : max-tree (MT)
pos_mt = dict(zip(nx_max_tree.nodes, [pos_cmt[node]
                                      for node in nx_max_tree.nodes]))

# plot the trees with networkx and matplotlib
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True, figsize=(20, 8))

plot_tree(nx_max_tree, pos_mt, ax1, title='Component tree',
          labels=labels_ct, font_size=6, text_size=8)

plot_tree(nx_max_tree, pos_mt, ax2, title='Max tree', labels=labels)

plot_tree(canonical_max_tree, pos_cmt, ax3, title='Canonical max tree')

fig.tight_layout()

plt.show()