
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  $a,b$  be real numbers such that  $|a| \neq |b|$  and  $\frac{a+b}{a-b}+\frac{a-b}{a+b}=6.$  Find the value of the expression  $\frac{a^3+b^3}{a^3-b^3}+\frac{a^3-b^3}{a^3+b^3}.$ 

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