
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 a triangle $\triangle ABC$, where $A$, $B$, $C$ are the three internal angles, and $a$, $b$, $c$ are the sides opposite to them respectively. If $2 \sqrt {2}(\sin ^{2}A-\sin ^{2}C)=(a-b)\sin B$, and the radius of the circumcircle of $\triangle ABC$ is $\sqrt {2}$,
$(1)$ Find angle $C$;
$(2)$ Find the maximum value of the area $S$ of $\triangle ABC$.

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