
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 vectors $\overrightarrow {a}=(\sin{\omega x} , 1)$ and $\overrightarrow {b}=( \sqrt {3} ,-\cos{\omega x})$, where $\omega > 0$, define the function $f(x) = \overrightarrow {a} \cdot \overrightarrow {b}$. The smallest positive period of $f(x)$ is $\pi$.

(I) Find the value of $\omega$;
(II) Find the interval(s) where $f(x)$ is monotonically increasing on $[0, \pi]$.

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