
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 $f(x)=\sin (\omega x+\varphi)$ $(\omega > 0,|\varphi|\leqslant \frac{\pi}{2})$, $x=- \frac{\pi}{4}$ is a zero of $f(x)$, and $x=\frac{\pi }{4}$ is the axis of symmetry for the graph of $y=f(x)$. If $f(x)$ is monotonic in the interval $( \frac{\pi}{18}, \frac{5\pi}{36})$, determine the maximum value of $\omega$.

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