
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 $f(x) = 5\sin x \cos x - 5\sqrt{3} \cos^2 x + \frac{5}{2}\sqrt{3}$, where $x$ belongs to the set of real numbers $\mathbb{R}$, find:
(1) The smallest positive period of the function $f(x)$;
(2) The intervals of monotonicity of the function $f(x)$;
(3) The axes of symmetry and the centers of symmetry of the graph of the function $f(x)$.

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