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

(1) Find the smallest positive period of $f(x)$.

(2) Given $\triangle ABC$ with angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively, and $f(C) = 0$, $c = 3$, $2\sin A - \sin B = 0$, find the values of $a$ and $b$.

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