
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 $$f(x)=\sin\left( \frac {1}{2}x+ \frac {\pi}{3}\right)$$  
(1) Find the smallest positive period and the maximum value of the function $f(x)$, and determine the value of $x$ at which $f(x)$ attains its maximum value;  
(2) Find the intervals of monotonic increase for the function $f(x)$ on \[-2\pi, 2\pi\].

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