
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 the zero point of $f(x)$, $x = \frac{\pi}{4}$ is the symmetry axis of the graph of $y = f(x)$, and $f(x)$ is monotonous on $(\frac{\pi}{18}, \frac{5\pi}{36})$, find the maximum value of $\omega$.

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