
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
The expression
\[
\frac{P+Q}{P-Q}-\frac{P-Q}{P+Q}
\]
where \( P = x^2+y^2 \) and \( Q = x^2-y^2 \), simplifies to which of the following?
**A)** \(\frac{x^2+y^2}{x^2-y^2}\) \
**B)** \(\frac{x^4-y^4}{x^2y^2}\) \
**C)** \(\frac{x^4+y^4}{x^2y^2}\) \
**D)** \(\frac{2x^2}{y^2-x^2}\) \
**E)** \(\frac{2x^4-y^4}{x^2y^2}\)

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