
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 $f(x)=2\cos (\omega x+\frac{π}{4})$. For $\forall x\in R$, $f(x)\leqslant f(\pi)$, and $f(x)$ is monotonically decreasing on the interval $[0, \frac{π}{6}]$. Determine the maximum value of $\omega$.

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