
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
\[
\frac{x + y}{x - y} - \frac{x - y}{x + y} = 3.
\]
Find
\[
\frac{x^4 + y^4}{x^4 - y^4} - \frac{x^4 - y^4}{x^4 + y^4}.
\]

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