
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 $f(x)$, $x= \frac {\pi}{4}$ is the axis of symmetry for the graph of $y=f(x)$, and $f(x)$ is monotonic in $( \frac {\pi}{18}, \frac {5\pi}{36})$, the maximum value of $\omega$ is \_\_\_\_\_\_.

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