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

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