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]


Affix grammar

An affix grammar is a kind of formal grammar; it is used to describe the syntax of languages, mainly computer languages, using an approach based on how natural language is typically described.

The grammatical rules of an affix grammar are those of a context-free grammar, except that certain parts in the nonterminals (the affixes) are used as arguments.  If the same affix occurs multiple times in a rule, its value must agree, i.e. it must be the same everywhere.  In some types of affix grammar, more complex relationships between affix values are possible.

Example 

We can describe an extremely simple fragment of English in the following manner:

 Sentence → Subject Predicate
 Subject → Noun
 Predicate → Verb Object
 Object → Noun
 
 Noun → John
 Noun → Mary
 Noun → children
 Noun → parents
 
 Verb → like
 Verb → likes
 Verb → help
 Verb → helps

This context-free grammar describes simple sentences such as

 John likes children
 Mary helps John
 children help parents
 parents like John

With more nouns and verbs, and more rules to introduce other parts of speech, a large range of English sentences can be described; so this is a promising approach for describing the syntax of English.

However, the given grammar also describes sentences such as

 John like children
 children helps parents

These sentences are wrong: in English, subject and verb have a grammatical number, which must agree.

An affix grammar can express this directly:
 Sentence → Subject + number  Predicate+number
 Subject + number → Noun + number
 Predicate + number → Verb + number  Object
 Object → Noun + number

 Noun + singular → John
 Noun + singular → Mary
 Noun + plural → children
 Noun + plural → parents
 
 Verb + singular → likes
 Verb + plural → like
 Verb + singular → helps
 Verb + plural → help

This grammar only describes correct English sentences, although it could be argued that
 John likes John
is still incorrect and should instead read
 John likes himself

This, too, can be incorporated using affixes, if the means of describing the relationships between different affix values are powerful enough. As remarked above, these means depend on the type of affix grammar chosen.

Types 

In the simplest type of affix grammar, affixes can only take values from a finite domain, and affix values can only be related through agreement, as in the example.
Applied in this way, affixes increase compactness of grammars, but do not add expressive power.

Another approach is to allow affixes to take arbitrary strings as values and allow   concatenations of affixes to be used in rules.  The ranges of allowable values for affixes can be described with context-free grammar rules.  This produces the formalism of two-level grammars, also known as Van Wijngaarden grammars or 2VW grammars.  These have been successfully used to describe complicated languages, in particular, the syntax of the Algol 68 programming language.  However, it turns out that, even though affix values can only be manipulated with string concatenation, this formalism is Turing complete; hence, even the most basic questions about the language described by an arbitrary 2VW grammar are undecidable in general.

Extended Affix Grammars, developed in the 1980s, are a more restricted version of the same idea.  They were mainly applied to describe the grammar of natural language, e.g. English.

Another possibility is to allow the values of affixes to be computed by code written in some programming language.  Two basic approaches have been used:
 In attribute grammars, the affixes (called attributes) can take values from arbitrary domains (e.g. integer or real numbers, complex data structures) and arbitrary functions can be specified, written in a language of choice, to describe how affix values in rules are derived from each other.
 In CDL (the Compiler Description Language) and its successor CDL2, developed in the 1970s, fragments of source code (usually in assembly language) can be used in rules instead of normal right-hand sides, allowing primitives for input scanning and affix value computations to be expressed directly.  Designed as a basis for practical compiler construction, this approach was used to write compilers, and other software, e.g. a text editor.

References 

Category:Formal languages
Category:Compiler construction
Category:Syntax
Category:Grammar frameworks