
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 $f(x) = \frac{x^2 + 1}{x^2 - 1}$. Find the expression for $f(-2x)$, given that $x^2 \neq 1$.
**A)** $\frac{4x^2 - 1}{4x^2 + 1}$  
**B)** $\frac{4x^2 + 1}{4x^2 - 1}$  
**C)** $\frac{x^2 - 1}{x^2 + 1}$  
**D)** $\frac{-4x^2 + 1}{4x^2 + 1}$

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