
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 $f\left(x\right)=\cos \left(\omega x+\varphi \right)\left(\omega\ \ \gt 0,0 \lt \varphi\ \ \lt \pi \right)$, if $f\left(x\right)$ is an odd function and monotonically decreasing on $(-\frac{π}{3},\frac{π}{6})$, then the maximum value of $\omega$ is ______.

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