
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 $\triangle ABC$, the sides opposite to angles A, B, and C are denoted as $a$, $b$, and $c$ respectively, and it is given that $$\frac {(a+b)^{2}-c^{2}}{3ab} = 1.$$  
(1) Find $\angle C$;  
(2) If $c= \sqrt {3}$ and $b= \sqrt {2}$, find $\angle B$ and the area of $\triangle ABC$.

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