
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
The equation \( \sin^2 x + \sin^2 3x + \sin^2 5x + \sin^2 6x = \frac{81}{32} \) can be reduced to the equivalent equation
\[ \cos ax \cos bx \cos cx = 0, \] for some positive integers \( a, \) \( b, \) and \( c. \) Find \( a + b + c. \)

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