
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 quadrilateral ABCD, the sides opposite angles A, B, and C are denoted as a, b, and c, respectively. Given vectors $$\overrightarrow {m} = (\sin A, \sin B - \sin C)$$ and $$\overrightarrow {n} = (a - \sqrt {3}b, b + c)$$, and that $$\overrightarrow {m}$$ is perpendicular to $$\overrightarrow {n}$$,  
(1) Find the value of angle C;  
(2) If the circumradius of triangle ABC is 2 and its area is $$\sqrt {3}$$, and a > b, find the values of a and b.

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