
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 $f(x) = \sin^2 x + \sqrt{3} \sin x \cos x, x \in R$.

(1) Find the value of $f(\frac{\pi}{12})$;

(2) Find the range of the function $f(x)$ on the interval $[0, \frac{\pi}{2}]$;

(3) Indicate the number of zeros of the function $f(x)$ on the interval $[0, 2\pi]$, and find the sum of these zeros.

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