
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
Let $f(x)=\cos(\omega x+\varphi)$, where $(\omega > 0, 0 < \varphi < \pi)$. If the smallest positive period of $f(x)$ is $T$, and $f(T)=\frac{\sqrt{3}}{2}$, and $x=\frac{π}{9}$ is a zero of $f(x)$, find the minimum value of $\omega$.

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