
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 number of solutions to
\[\cos 6x + \cos^2 4x + \cos^3 3x + \cos^4 2x = 0\]
for $-\pi \le x \le \pi.$

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