
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
In triangle $ABC$, with internal angles $A$, $B$, and $C$ opposite sides $a$, $b$, and $c$ respectively, it is given that the function $$f(x)=\sin(2x+B)+ \sqrt {3}\cos(2x+B)$$ is an even function, and $$b=f\left(\frac {\pi}{12}\right)$$.
(1) Find the value of $b$.
(2) If $a=3$, find the area $S$ of triangle $ABC$.

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