
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 $f(x)=\sqrt{3}\cos^2{\omega}x+\sin{\omega}x\cos{\omega}x (\omega>0)$, if there exists a real number $x_{0}$ such that for any real number $x$, $f(x_{0})\leq f(x)\leq f(x_{0}+2022\pi)$ holds, then the minimum value of $\omega$ is ____.

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