
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
The function $f(x)=\cos(\omega x+\varphi)(0 < \varphi < \pi)$ has a period of $T=\frac{2\pi}{3}$. Its graph is symmetric about $(\frac{\pi}{18},0)$, and when $x\in [\frac{\pi}{6},m]$, the range of $f(x)$ is $[-1,-\frac{\sqrt{3}}{2}]$. Determine the range of values for $m$.

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