
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 $f(x) = 2\cos{x} (\sqrt{3}\sin{x}+\cos{x})+m$, where $x\in\mathbb{R}$ and $m\in\mathbb{R}$.
(1) Find the smallest positive period of $f(x)$.
(2) If the maximum value of $f(x)$ on the interval $[0, \frac{\pi}{2}]$ is 6, find the minimum value of $f(x)$ on the interval $[0, \frac{\pi}{2}]$.

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