
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
Solve the equation

$$
\cos ^{2} 8 x+\cos ^{2} x=2 \cos ^{2} x \cdot \cos ^{2} 8 x
$$

In the answer, indicate the number equal to the sum of the roots of the equation that belong to the interval $[3 \pi ; 6 \pi]$, rounding this number to two decimal places if necessary.

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