
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 $f(x)=\sin x\cos x-\sqrt{3}\cos^{2}x+\dfrac{\sqrt{3}}{2}\ (x\in\mathbb{R})$.
(1) Find the smallest positive period of $f(x)$;
(2) Find the equation of the symmetry axis and the coordinates of the symmetry center of the graph of $f(x)$.

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