
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 $\overrightarrow{a} = (2\sin x, \cos x)$ and $\overrightarrow{b} = (\cos x, 2\sqrt{3}\cos x)$, and the function $f(x) = \overrightarrow{a}\cdot\overrightarrow{b}$
(I) Find the smallest positive period of the function $f(x)$;
(II) When $x\in[0, \frac{\pi}{2}]$, find the maximum and minimum values of the function $f(x)$.

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