
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 $\overrightarrow{a}=(2\sin x,1)$ and $\overrightarrow{b}=(2\cos (x-\frac{\pi }{3}),\sqrt{3})$, let $f(x)=\overrightarrow{a}\bullet \overrightarrow{b}-2\sqrt{3}$.

(I) Find the smallest positive period and the zeros of $f(x)$;

(II) Find the maximum and minimum values of $f(x)$ on the interval $[\frac{\pi }{24},\frac{3\pi }{4}]$.

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