
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 that the graph of $f(x) = \cos \omega x$ ($\omega > 0$) is symmetric about the point $\left( \frac{3\pi}{4}, 0 \right)$, and $f(x)$ is monotonic in the interval $\left( 0, \frac{2\pi}{3} \right)$, find the value of $\omega$.

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