
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 \( u \) and \( v \) be complex numbers such that
\[
\frac{u^3 + v^3}{u^3 - v^3} + \frac{u^3 - v^3}{u^3 + v^3} = 2.
\]
Find
\[
\frac{u^9 + v^9}{u^9 - v^9} + \frac{u^9 - v^9}{u^9 + v^9}.
\]

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