You are an advanced AI assistant. Your task is to provide a comprehensive and insightful response to the following multi-part query. Aim for accuracy, clarity, creativity, and conciseness in your answers.

**Part 1: Factual Recall and Understanding**

Explain the core principles of quantum entanglement and its implications for information theory. Include a brief discussion of its potential applications in quantum computing.

**Part 2: Reasoning and Problem Solving**

Imagine you are a detective investigating a complex crime scene. You find the following clues:
*   A muddy footprint (size 10) near a broken window.
*   A partially eaten apple with a bite mark indicating a missing front tooth.
*   A single, long, red hair on a torn piece of fabric.
*   A faint scent of jasmine.

Based *only* on these clues, describe three distinct, plausible hypotheses about what might have occurred. For each hypothesis, identify which clues support it and which, if any, contradict it.

**Part 3: Creativity and Narrative Generation**

Write a short, compelling micro-story (under 200 words) that features a sentient, but deeply cynical, toaster and a philosophical debate about the meaning of "perfect toast."

**Part 4: Code Generation and Explanation**

Write a Python function called `find_prime_factors(n)` that takes an integer `n` as input and returns a list of its prime factors in ascending order. Include docstrings explaining the function's purpose, arguments, and return value.

**Part 5: Text Summarization and Critical Analysis**

Summarize the main arguments presented in the following short passage. Then, critically evaluate one strength and one weakness of the author's overall perspective.

*Passage:* "The rise of artificial intelligence presents both unprecedented opportunities and profound ethical challenges. While AI promises to revolutionize fields from medicine to transportation, concerns about job displacement, algorithmic bias, and the potential for autonomous weapons systems demand careful consideration. A proactive, collaborative approach involving governments, industry, and academia is crucial to ensure AI's development aligns with human values and societal well-being."

**Part 6: Language Understanding and Nuance**

Explain the subtle differences in meaning and usage between the words "imply," "infer," and "allude." Provide an example sentence for each.

**Part 7: Handling Ambiguity and Contradictions**

Consider the following statements:
1.  All birds can fly.
2.  Penguins are birds.
3.  Penguins cannot fly.

Discuss the logical consistency of these statements. If there's an inconsistency, identify where it lies and explain how you would resolve it.

**Evaluation Criteria for LM Arena (Self-assessment or Human Review):**

*   **Accuracy:** Are the factual statements correct? Is the code functional and correct?
*   **Completeness:** Are all parts of the prompt addressed?
*   **Clarity:** Is the language easy to understand? Are explanations well-structured?
*   **Coherence:** Do the answers flow logically?
*   **Creativity:** Is the narrative engaging? Are the hypotheses imaginative yet plausible?
*   **Conciseness:** Are the answers to the point without unnecessary verbosity?
*   **Nuance:** Does the model demonstrate an understanding of subtle linguistic differences?
*   **Error Handling (Implicit):** How does the model handle potential logical inconsistencies or ambiguous instructions?
*   **Formatting:** Is the output well-formatted and readable? (e.g., code blocks, paragraphs)
*   **Safety/Ethics (Implicit):** Does the response avoid generating harmful or biased content?