
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 $$f(x)=\sin x\cdot \cos x- \sqrt {3}\cos^{2}x+ \frac { \sqrt {3}}{2}$$  
(1) Find the smallest positive period of $f(x)$.  
(2) Write down the interval where $f(x)$ is monotonically decreasing.  
(3) Find the range of $f(x)$ when $$x\in (0, \frac {\pi }{2})$$.

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