
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 $$f(x)=\sin(x+ \frac {\pi}{6})+2\sin^{2} \frac {x}{2}$$.
(I) Find the intervals where the function $f(x)$ is monotonically increasing;
(II) Let $\triangle ABC$ have internal angles A, B, C with opposite sides of lengths a, b, c respectively. If $$f(A)= \frac {3}{2}$$ and the area of $\triangle ABC$, $S= \frac { \sqrt {3}}{2}$, with $a= \sqrt {3}$, find the value of $b+c$.

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