
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 $$f(x)=2\cos x(\cos x+ \sqrt {3}\sin x)$$ (where $x\in\mathbb{R}$).  
(1) Find the period of the function $y=f(x)$ and the intervals where it is monotonically increasing;  
(2) When $$x\in[0, \frac {\pi}{2}]$$, find the maximum value of the function $f(x)$.

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