
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 $f(x)=2\sin (\omega x+\phi)$ $(\omega > 0,0 < \phi < \frac {\pi}{2})$, $f(- \frac {\pi}{4})=0$, $f( \frac {\pi}{4}-x)=f( \frac {\pi}{4}+x)$, and $f(x)$ is monotonic on $( \frac {\pi}{18}, \frac {2\pi}{9})$, the maximum value of $\omega$ is \_\_\_\_\_\_.

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