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

(1) Find the minimum value and the smallest positive period of the function $f(x)$;

(2) In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, with $c= \sqrt{3}$, $f(C)=0$. If vectors $m=(1,\sin A)$ and $n=(2,\sin B)$ are collinear, find the values of $a$ and $b$.

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