
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
Given the equation $\sin^2 x + \sin^2 3x + \sin^2 5x + \sin^2 7x = 2$, reduce it to an equivalent equation of the form \[\cos ax \cos bx \cos cx = 0,\] 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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