
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 \( F = \log \frac{1+x}{1-x} \). Define a new function \( G \) by replacing each \( x \) in \( F \) by \( \frac{2x - x^2}{1+2x^2} \) and simplify. What does the simplified expression \( G \) equal?
A) \( -F \)  
B) \( F \)  
C) \( 2F \)  
D) \( \frac{F}{2} \)  
E) \( F^2 \)

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