
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
Let \( f(x) = \frac{x^2 + 2x + 1}{x^2 - 2x + 1} \) and \( g(x) = x^2 \). Determine \( g(f(-x)) \) for \( x^2 \neq 1 \).
**A)** \(\frac{(x^2 + 2x + 1)^2}{(x^2 - 2x + 1)^2}\)
**B)** \(\frac{(x^2 - 2x + 1)^2}{(x^2 + 2x + 1)^2}\)
**C)** \(x^4\)
**D)** \(1\)

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