
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
Let the function be $$f(x)=\sin(2x+ \frac {\pi}{3})+ \sqrt {3}-2 \sqrt {3}\cos^{2}x+1$$  
(1) Find the smallest positive period of $f(x)$ and the symmetry center of its graph;  
(2) Find the intervals where $f(x)$ is monotonically increasing.

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