
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 $f(x)=2\sin x\cos x-\sqrt{3}\cos 2x+1$ $(x\in \mathbb{R})$.

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

(II) Find the maximum and minimum values of $f(x)$ in the interval $x\in \left[\frac{\pi }{4},\frac{\pi }{2}\right]$;

(III) If the inequality $\left[f(x)-m\right]^{2} < 4$ holds for any $x\in \left[\frac{\pi }{4},\frac{\pi }{2}\right]$, find the range of the real number $m$.

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