
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 $f(x)=\sin (\omega x+ \frac{\pi}{6})-\cos \omega x$ $(\omega > 0)$. If the graph of $f(x)$ is symmetric about the line $x=2\pi$, and it is a monotonic function in the interval $\left[- \frac{\pi}{4}, \frac{\pi}{4}\right]$, then the set of values for $\omega$ is $\boxed{\text{answer}}$.

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