
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
Consider the expression
\[
\frac{A+B}{A-B}+\frac{A-B}{A+B}
\]
where \( A = x^2 \) and \( B = y^2 \). Simplify the expression and find its equivalent form.
A) \( \frac{x^4 + y^4}{x^2 + y^2} \)
B) \( \frac{2(x^4 + y^4)}{x^4 - y^4} \)
C) \( \frac{x^4 - y^4}{x^4 + y^4} \)
D) \( \frac{x^2 + y^2}{x^4 - y^4} \)
E) \( \frac{x^4 + y^4}{x^4 - y^4} \)

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