
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 $f(x) = \sin^2x + 2\sqrt{3}\sin x\cos x + 3\cos^2x$, where $x \in \mathbb{R}$. Find:  
(I) The smallest positive period of the function $f(x)$.  
(II) The range of $f(x)$ in the interval $\left[-\frac{\pi}{6}, \frac{\pi}{3}\right]$.  
(III) Describe how to transform the graph of $y=\sin x$ to obtain the graph of the function $f(x)$.

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