
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
A mustache is created by taking the set of points  $(x, y)$  in the  $xy$ -coordinate plane that satisfy  $4 + 4 \cos(\pi x/24) \le y \le 6 + 6\cos(\pi x/24)$  and  $-24 \le x \le 24$ .  What is the area of the mustache?

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