
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 $f(x)=\sin (2x+ \frac {\pi}{6})+\cos 2x$.  
(I) Find the interval of monotonic increase for the function $f(x)$;  
(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$. Given that $f(A)= \frac { \sqrt {3}}{2}$, $a=2$, and $B= \frac {\pi}{3}$, find the area of $\triangle ABC$.

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