
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
If
\[\frac{\tan^2 \theta}{a} + \frac{\cot^2 \theta}{b} = \frac{1}{2(a + b)},\] then find the value of
\[\frac{\tan^6 \theta}{a^2} + \frac{\cot^6 \theta}{b^2}\] in terms of $a$ and $b.$

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