
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 in triangle $\triangle ABC$, the internal angles $A$, $B$, and $C$ satisfy $\frac{\sin A - \sin B + \sin C}{\sin C} = \frac{\sin B}{\sin A + \sin B - \sin C}$. Find:<br/>
$(1)$ the angle $A$;<br/>
$(2)$ 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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