
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 area of the region bound by the equations  $y = 2\cos(4x)$ ,  $y = \sin(2x) + 10$ ,  $x=0$ , and  $x = 5\pi$  can be expressed as  $x\pi$  for some value of  $x$ . Evaluate  $x$ .

*2022 CCA Math Bonanza Lightning Round 1.3*

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