
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 $f(x)=\frac{1}{2}\sin 2x-\sqrt{3}\cos ^{2}x.$
(I) Find the minimum period and minimum value of $f(x)$;
(II) Stretch the horizontal coordinate of each point on the graph of the function $f(x)$ to twice its original length, and keep the vertical coordinate unchanged to obtain the graph of function $g(x)$. Find the range of $g(x)$ when $x\in[\frac{\pi}{2},\pi]$.

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