
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 \( P = 2x + 3y \) and \( Q = x - 2y \), simplifies to:
A) \( \frac{8x^2 - 4xy - 24y^2}{3x^2 + 16xy + 5y^2} \)
B) \( \frac{8x^2 + 4xy - 24y^2}{3x^2 + 16xy + 5y^2} \)
C) \( \frac{8x^2 - 4xy + 24y^2}{3x^2 + 16xy + 5y^2} \)
D) \( \frac{8x^2 + 24y^2}{3x^2 + 16xy + 5y^2} \)
E) \( \frac{-8x^2 + 24y^2}{3x^2 + 16xy + 5y^2} \)

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