
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
Given the function $f(x)=\cos(\omega x+\phi)$ $(\omega>0, |\phi|<\frac{\pi}{2})$ with a minimum positive period of $\pi$, and its graph is symmetric about the line $x=-\frac{\pi}{12}$, then the function $y=f(x)$ has exactly ______ zero points for $x\in[-2\pi, 2\pi]$.

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