
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given \( P_{1}(x) = x^{2} - 2 \) and \( P_{i}(x) = P_{1}\left[P_{i-1}(x)\right] \) for \( i = 2, 3, \cdots, n \), solve for \( P_{n}(x) = x \).

Present the answer in LaTex format: \boxed{Your answer}
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