
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 $$f(x)= \sqrt {3}\sin \frac {x}{2}\cos \frac {x}{2}+\cos^{2} \frac {x}{2}- \frac {1}{2}$$, and in triangle ABC, the sides opposite angles A, B, and C are denoted as a, b, and c respectively.  
(I) Find the intervals of increase for $f(x)$.  
(II) If $f(B+C)=1$ and $$a= \sqrt {3},b=1$$, find the magnitude of angle C.

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