
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 \(H = \log_2 \frac{1-x}{1+x}\). Find a new function \(I\) by replacing each \(x\) in \(H\) by \(\frac{2x-x^2}{1+2x^2}\), and simplify. What is the simplified expression \(I\) equal to?
A) $-H$
B) $H$
C) $2H$
D) $\log_2 H$
E) $\frac{H}{2}$

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