
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 $f(x)=\sin (2\omega x-\frac{\pi }{6})-4{\sin }^{2}\omega x+2\quad (\omega >0)$ with the smallest positive period of $\pi$.

(1) Find the value of $\omega$;

(2) Find the interval(s) where the function $f(x)$ is monotonically increasing on $[0,\frac{3\pi }{4}]$.

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