
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
\[\frac{\sin^6 \theta}{a} + \frac{\cos^6 \theta}{b} = \frac{1}{a + b},\]
then find the value of 
\[\frac{\sin^{12} \theta}{a^2} + \frac{\cos^{12} \theta}{b^2}\]
in terms of $a$ and $b.$

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