
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 $f(x) = \cos(\omega x + \varphi)$ ($\omega > 0$), where $x = -\frac{\pi}{8}$ is a zero of $y = f(x)$, and the line $x = \frac{3\pi}{8}$ is an axis of symmetry for the graph of $y = f(x)$. Also, the function $f(x)$ is monotonic in the interval $\left(\frac{\pi}{12}, \frac{5\pi}{24}\right)$. Calculate the maximum value of $\omega$.

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