
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 $f(x)=\sin x\cos x-\sqrt{3}\sin^2 x$,
(I) Find the value of $f(\frac{\pi}{6})$;
(II) Suppose $\alpha\in(0,\pi)$, and $f(\frac{\alpha}{2})=\frac{1}{4}-\frac{\sqrt{3}}{2}$, find the value of $\sin\alpha$.

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