
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 $f(x)=\frac{1}{2}\cos 2\omega x+\sqrt{3}\sin \omega x\cos \omega x(\omega > 0)$, its smallest positive period is $\pi$.

(1) Find the value of $f(\frac{2\pi }{3})$;

(2) Find the monotonically increasing interval of the function $f(x)$ and the equation of the symmetry axis of its graph.

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