
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 $$f(x)=2 \sqrt {3}\sin(x+ \frac {\pi}{4})\cos(x+ \frac {\pi}{4})+\sin2x$$.
(1) Find the intervals of monotonic increase for the function $f(x)$;
(2) If the graph of $f(x)$ is translated to the left by $$\frac {\pi}{6}$$ units to obtain the graph of function $g(x)$, find the maximum and minimum values of function $g(x)$ in the interval $$[0, \frac {\pi}{2}]$$.

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