
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 that the internal angles A, B, and C of triangle ABC satisfy $$\frac {sinA-sinB+sinC}{sinC}$$ = $$\frac {sinB}{sinA+sinB-sinC}$$.
(1) Find angle A;
(2) If the radius of the circumcircle of triangle ABC is 1, find the maximum value of the area S of triangle ABC.

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