
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
Suppose \( g(x) = \log \left(\frac{1+x}{1-x}\right) \) is defined for \( -1 < x < 1 \). Determine \( g\left(\frac{4x+x^2}{1+4x+x^2}\right) \) in terms of \( g(x) \).
A) \( g(x) \)
B) \( 2g(x) \)
C) \( g(2x) \)
D) \( -g(x) \)
E) \( g(x)^2 \)

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