
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 \( F = \lg \frac{1+x}{1-x} \). If each \( x \) in the expression is replaced by \( \frac{3x + x^3}{1 + 3x^2} \), determine the simplified form of the new function \( G \).

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