
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 $f(x)=\cos (\omega x+\varphi)$ ($\omega > 0$, $|\varphi| \leqslant \frac {\pi}{2}$), when $x=- \frac {\pi}{4}$, the function $f(x)$ can achieve its minimum value, and when $x= \frac {\pi}{4}$, the function $y=f(x)$ can achieve its maximum value. Moreover, $f(x)$ is monotonic in the interval $( \frac {\pi}{18}, \frac {5\pi}{36})$. Find the value of $\varphi$ when $\omega$ takes its maximum value.

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