
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 $f(x)=\cos^2 \frac{x}{2}-\sin \frac{x}{2}\cos \frac{x}{2}- \frac{1}{2}$.
- (I) Find the smallest positive period and the range of the function $f(x)$;
- (II) If $f(\alpha)= \frac{3 \sqrt{2}}{10}$, find the value of $\sin 2\alpha$.

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