
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 \( x \) and \( y \) be complex numbers such that
\[
\frac{x+y}{x-y} + \frac{x-y}{x+y} = 2.
\]
Find
\[
\frac{x^6 + y^6}{x^6 - y^6} + \frac{x^6 - y^6}{x^6 + y^6}.
\]

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