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]


from pm4py.objects.process_tree import process_tree
from pm4py.objects.process_tree import pt_operator
from scipy.stats import triang as triangular
import string
import math
import itertools
from enum import Enum
from itertools import accumulate as _accumulate, repeat as _repeat
from bisect import bisect as _bisect
import random


def choices(population, weights=None, *, cum_weights=None, k=1):
    """Return a k sized list of population elements chosen with replacement.
    If the relative weights or cumulative weights are not specified,
    the selections are made with equal probability.
    """
    n = len(population)
    if cum_weights is None:
        if weights is None:
            _int = int
            n += 0.0    # convert to float for a small speed improvement
            return [population[_int(random.random() * n)] for i in _repeat(None, k)]
        cum_weights = list(_accumulate(weights))
    elif weights is not None:
        raise TypeError('Cannot specify both weights and cumulative weights')
    if len(cum_weights) != n:
        raise ValueError('The number of weights does not match the population')
    bisect = _bisect
    total = cum_weights[-1] + 0.0   # convert to float
    hi = n - 1
    return [population[bisect(cum_weights, random.random() * total, 0, hi)]
            for i in _repeat(None, k)]


class Parameters(Enum):
    SEQUENCE = "sequence"
    CHOICE = "choice"
    PARALLEL = "parallel"
    LOOP = "loop"
    OR = "or"
    MODE = "mode"
    MIN = "min"
    MAX = "max"
    SILENT = "silent"
    DUPLICATE = "duplicate"
    LT_DEPENDENCY = "lt_dependency"
    INFREQUENT = "infrequent"
    NO_MODELS = "no_models"
    UNFOLD = "unfold"
    MAX_REPEAT = "max_repeat"


def apply(parameters=None):
    """
    Generate a process tree using the PTAndLogGenerator approach
    (see the paper PTandLogGenerator: A Generator for Artificial Event Data)

    Parameters
    --------------
    parameters
        Parameters of the algorithm, according to the paper:
        - Parameters.MODE: most frequent number of visible activities
        - Parameters.MIN: minimum number of visible activities
        - Parameters.MAX: maximum number of visible activities
        - Parameters.SEQUENCE: probability to add a sequence operator to tree
        - Parameters.CHOICE: probability to add a choice operator to tree
        - Parameters.PARALLEL: probability to add a parallel operator to tree
        - Parameters.LOOP: probability to add a loop operator to tree
        - Parameters.OR: probability to add an or operator to tree
        - Parameters.SILENT: probability to add silent activity to a choice or loop operator
        - Parameters.DUPLICATE: probability to duplicate an activity label
        - Parameters.LT_DEPENDENCY: probability to add a random dependency to the tree
        - Parameters.INFREQUENT: probability to make a choice have infrequent paths
        - Parameters.NO_MODELS: number of trees to generate from model population
        - Parameters.UNFOLD: whether or not to unfold loops in order to include choices underneath in dependencies: 0=False, 1=True
            if lt_dependency <= 0: this should always be 0 (False)
            if lt_dependency > 0: this can be 1 or 0 (True or False)
        - Parameters.MAX_REPEAT: maximum number of repetitions of a loop (only used when unfolding is True)
    """
    if parameters is None:
        parameters = {}

    if not "mode" in parameters:
        parameters["mode"] = 20
    if not "min" in parameters:
        parameters["min"] = 10
    if not "max" in parameters:
        parameters["max"] = 30
    if not "sequence" in parameters:
        parameters["sequence"] = 0.25
    if not "choice" in parameters:
        parameters["choice"] = 0.25
    if not "parallel" in parameters:
        parameters["parallel"] = 0.25
    if not "loop" in parameters:
        parameters["loop"] = 0.25
    if not "or" in parameters:
        parameters["or"] = 0.0
    if not "silent" in parameters:
        parameters["silent"] = 0.2
    if not "duplicate" in parameters:
        parameters["duplicate"] = 0
    if not "lt_depencency" in parameters:
        parameters["lt_depencency"] = 0.0
    if not "infrequent" in parameters:
        parameters["infrequent"] = 0.5
    if not "no_models" in parameters:
        parameters["no_models"] = 10
    if not "unfold" in parameters:
        parameters["unfold"] = 10
    if not "max_repeat" in parameters:
        parameters["max_repeat"] = 10

    return GeneratedTree(parameters).generate()

def assign_operator(operator):
    if operator == "choice":
        return pt_operator.Operator.XOR
    elif operator == "sequence":
        return pt_operator.Operator.SEQUENCE
    elif operator == "parallel":
        return pt_operator.Operator.PARALLEL
    elif operator == "or":
        return pt_operator.Operator.OR
    elif operator == "loop":
        return pt_operator.Operator.LOOP
    else:
        return None


class GeneratedTree(object):
    # are later used as labels
    alphabet = string.ascii_lowercase

    def calculate_activity_distribution(self, mode, min, max):
        """
        Here, the triangular function is used, since the parameters for this function are given in the paramterfile.
        However, this approach can be applied on other distribution functions as well.
        :param mode: Mode of the distribution
        :param min: Smallest number
        :param max: Highest number
        :return: Distribution object
        """
        c = (mode - min) / (max - min)
        return triangular(c, loc=min, scale=max - min)

    def draw_random_number_from_distribution(self):
        return self.activity_distribution.rvs(1)[0]

    def select_operator(self):
        # add root operator, if probabilities are high enough
        # ordering of operator computation is sequence, choice, parallel, loop, or
        operator = choices(["sequence", "choice", "parallel", "loop", "or"],
                                  [self.parameters["sequence"], self.parameters["choice"], self.parameters["parallel"],
                                   self.parameters["loop"], self.parameters["or"]])
        return operator[0]

    def get_next_activity(self, activity):
        result = self.set_activity_labels[self.set_activity_labels.index(activity) + 1]
        return result

    def assign_root_opeartor(self):
        activity = "a"
        # is a silent activity chosen
        silent_activity = False
        if random.random() < self.parameters["silent"]:
            silent_activity = True
        root = self.tree._get_root()
        operator = self.select_operator()
        root.operator = assign_operator(operator)
        # if operator is loop, we use a special structure, otherwise 2
        if operator == "loop":
            root.operator = pt_operator.Operator.SEQUENCE
            root_loop = process_tree.ProcessTree(operator=pt_operator.Operator.LOOP)
            root_loop.parent = root
            root._children.append(root_loop)
            new_node = process_tree.ProcessTree(label=activity)
            new_node.parent = root_loop
            root_loop._children.append(new_node)
            activity = self.get_next_activity(activity)
            if silent_activity:
                new_node = process_tree.ProcessTree(label=None)
                new_node.parent = root_loop
                root_loop._children.append(new_node)

            else:
                new_node = process_tree.ProcessTree(label=activity)
                new_node.parent = root_loop
                root_loop._children.append(new_node)
                activity = self.get_next_activity(activity)
            new_node = process_tree.ProcessTree(label=activity)
            new_node.parent = root
            root._children.append(new_node)
            self.total_activities -= 1
        else:
            if silent_activity and operator == "choice":
                number = random.choice([0, 1])
                if number == 0:
                    new_node = process_tree.ProcessTree(label=None)
                    new_node.parent = root
                    root._children.append(new_node)
                    new_node = process_tree.ProcessTree(label=activity)
                    new_node.parent = root
                    root._children.append(new_node)
                else:
                    new_node = process_tree.ProcessTree(label=activity)
                    new_node.parent = root
                    root._children.append(new_node)
                    new_node = process_tree.ProcessTree(label=None)
                    new_node.parent = root
                    root._children.append(new_node)
            else:
                new_node = process_tree.ProcessTree(label=activity)
                new_node.parent = root
                root._children.append(new_node)
                activity = self.get_next_activity(activity)
                new_node = process_tree.ProcessTree(label=activity)
                new_node.parent = root
                root._children.append(new_node)
        # always two children are added
        self.total_activities -= 2
        return self.get_next_activity(activity)

    def add_node(self, next_activity):
        """
        Add nodes to current tree. The general procedure is as follows:
        Select a random leaf (leaves have label). Next step, and opertor is chosen.
        The chosen operator then replaces the leaf, whereby the old label is then add as a leaf to the manipulated node.
        Then, next activity is added as a second leaf to the new operator node or a silent acticity (tau) is added.
        :return: Next activity
        """
        # Need to select random node that is not a silent activity
        leaf_silent = True
        while (leaf_silent):
            leaf = random.choice(self.tree._get_leaves())
            if leaf.label is not None:
                leaf_silent = False
        operator_nok = True
        while (operator_nok):
            operator = self.select_operator()
            if self.total_activities > 1:
                operator_nok = False
            else:
                if operator != "loop":
                    operator_nok = False
        activity = leaf._get_label()
        leaf._set_label(None)
        leaf._set_operator(assign_operator(operator))
        # Will be an tau added?
        silent_activity = False
        if random.random() < self.parameters["silent"]:
            silent_activity = True
        # add two children
        if operator == "loop":
            leaf._set_operator(pt_operator.Operator.SEQUENCE)
            root_loop = process_tree.ProcessTree(pt_operator.Operator.LOOP)
            root_loop.parent = leaf
            leaf._children.append(root_loop)
            new_node = process_tree.ProcessTree(label=activity)
            new_node.parent = root_loop
            root_loop._children.append(new_node)
            activity = next_activity
            if silent_activity:
                new_node = process_tree.ProcessTree(label=None)
                new_node.parent = root_loop
                root_loop._children.append(new_node)
            else:
                new_node = process_tree.ProcessTree(label=activity)
                new_node.parent = root_loop
                root_loop._children.append(new_node)
                activity = self.get_next_activity(activity)
            new_node = process_tree.ProcessTree(label=activity)
            new_node.parent = leaf
            leaf._children.append(new_node)
            self.total_activities -= 1
        else:
            if silent_activity and operator == "choice":
                number = random.choice([0, 1])
                if number == 0:
                    new_node = process_tree.ProcessTree(label=None)
                    new_node.parent = leaf
                    leaf._children.append(new_node)
                    new_node = process_tree.ProcessTree(label=activity)
                    new_node.parent = leaf
                    leaf._children.append(new_node)
                else:
                    new_node = process_tree.ProcessTree(label=activity)
                    new_node.parent = leaf
                    leaf._children.append(new_node)
                    new_node = process_tree.ProcessTree(label=None)
                    new_node.parent = leaf
                    leaf._children.append(new_node)
            else:
                new_node = process_tree.ProcessTree(label=activity)
                new_node.parent = leaf
                leaf._children.append(new_node)
                activity = next_activity
                new_node = process_tree.ProcessTree(label=activity)
                new_node.parent = leaf
                leaf._children.append(new_node)

        self.total_activities -= 2
        if silent_activity and operator == "choice":
            return next_activity
        else:
            return self.get_next_activity(activity)

    def add_duplicates(self):
        """
        Replaces some leaves  to add duplicated labels. Depends on parameter.
        :return:
        """
        duplication_allowed = False
        leaves = self.tree._get_leaves()
        for leaf in leaves:
            if leaf._parent != self.tree._get_root():
                duplication_allowed = True
                break
        # if there is at least a depth of two
        if duplication_allowed:
            # list that contains the leaves with a label unequal to tau
            leaves_with_label = []
            for leaf in leaves:
                if leaf.label is not None:
                    leaves_with_label.append(leaf)
            # generate random list of duplicates
            duplicates = []
            for leaf in leaves:
                if random.random() < self.parameters["duplicate"]:
                    duplicates.append(leaf)
            if len(duplicates) > 0:
                # select potential leaves to replace them by duplicates
                possible_replacements = []
                for leaf in leaves:
                    if leaf not in duplicates:
                        possible_replacements.append(leaf)
            for leaf in duplicates:
                i = 0
                siblings = []
                # determine sibling nodes (same parent)
                p = leaf._parent
                for child in p._children:
                    if child != leaf:
                        siblings.append(child)
                # TODO Skaling? Original: 30times, my idea : percentage of duplicates * len(leaves)
                while i < self.parameters["duplicate"] * len(leaves):
                    replacement = random.choice(possible_replacements)
                    if replacement not in siblings:
                        replacement._label = leaf._label
                        break

    def create_process_tree(self):
        self.tree = process_tree.ProcessTree()
        self.set_activity_labels = []
        p = 1
        # create labels
        while (self.total_activities > len(self.set_activity_labels)):
            # pairwise product
            l = itertools.product(self.alphabet, repeat=p)
            for item in l:
                label = ""
                for element in item:
                    label += str(element)
                self.set_activity_labels.append(label)
            p += 1
        step = 1
        activity = self.assign_root_opeartor()
        step += 1

        while (self.total_activities > 0):
            activity = self.add_node(activity)
            step += 1

    def __init__(self, parameters):
        self.parameters = {}
        for param in parameters:
            p = param if type(param) is str else param.value
            self.parameters[p] = parameters[param]
        # rescale probabilities of operators if the sum is not equal to one
        if self.parameters["sequence"] + self.parameters["choice"] + self.parameters["parallel"] + self.parameters[
            "loop"] + self.parameters["or"] != 1:
            sum_of_operators = self.parameters["sequence"] + self.parameters["choice"] + self.parameters["parallel"] + \
                               self.parameters["loop"] + self.parameters["or"]
            self.parameters["sequence"] = self.parameters["sequence"] / sum_of_operators
            self.parameters["choice"] = self.parameters["choice"] / sum_of_operators
            self.parameters["parallel"] = self.parameters["parallel"] / sum_of_operators
            self.parameters["or"] = self.parameters["or"] / sum_of_operators
            self.parameters["loop"] = self.parameters["loop"] / sum_of_operators
        # First step: Compute acivity distribution
        # Since mode, min and max are given, the triangle distribution is chosen
        self.activity_distribution = self.calculate_activity_distribution(self.parameters["mode"],
                                                                          self.parameters["min"],
                                                                          self.parameters["max"])
        # Number of total activities represented in the tree. Also, tau is counted as an activity.
        self.total_activities = int(math.ceil(self.draw_random_number_from_distribution()))


    def generate(self):
        # Create a process tree based on the given probabilities
        self.create_process_tree()
        # add duplicates
        self.add_duplicates()

        return self.tree