
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 $f(x)=\sin(\omega x+\varphi)$ ($\omega\ \ \gt 0$, $|φ|≤\frac{π}{2}$). If $x=-\frac{π}{8}$ is a zero of the function $f(x)$, and $x=\frac{π}{8}$ is an axis of symmetry of the function $f(x)$, and $f(x)$ is monotonically increasing on the interval $({\frac{π}{5},\frac{π}{4}})$, then the maximum value of $\omega$ is ______.

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