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

(1) Find the value of $\omega$ and the interval where the function is monotonically increasing;
(2) Find the maximum and minimum values of the function $f(x)$ on the interval $[0, \dfrac{2\pi}{3}]$.

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