
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
Find the sum of all positive real solutions \( x \) to the equation 
\[ 4\cos\left(3x\right) \left(\cos\left(3x\right) - \cos\left(\frac{2016\pi^2}{x}\right)\right) = \cos\left(6x\right) - 1, \]
where \( x \) is measured in radians.

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