
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 $f(x) = \cos(\omega x + \varphi)$ ($\omega > 0$, $-\pi \leq \varphi \leq 0$) is an odd function, and it is monotonic in the interval $\left[-\frac{\pi}{4}, \frac{3\pi}{16}\right]$, the range of $\omega$ is \_\_\_\_\_\_.

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