
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 minimum positive period of the function $f(x)=2\sqrt{3}\cos \omega x\cos (\omega x+\dfrac{\pi }{2})+2{{\sin }^{2}}\omega x(\omega > 0)$ is $\pi$.

(1) Find the value of $\omega$ and the interval where the function $f(x)$ is monotonically increasing;

(2) Find the range of the function $f(x)$ on the interval $[\dfrac{\pi }{3}, \pi ]$.

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