
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
Let the function $f(x) = \vec{a} \cdot \vec{b}$, where the vectors $\vec{a} = (2\cos{x}, 1)$ and $\vec{b} = (\cos{x}, \sqrt{3}\sin{2x} + m)$.

(I) Find the smallest positive period of the function $f(x)$ and the interval(s) on which $f(x)$ is monotonically increasing within $[0, \pi]$.

(II) Given that $-4 < f(x) < 4$ holds true when $x \in \left[0, \frac{\pi}{6}\right]$, determine the range of values for the real number $m$.

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