
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 $\triangle ABC$, let $A$, $B$, and $C$ be the three interior angles, and $a$, $b$, and $c$ be the sides opposite these angles, respectively. Given that: 
\[2 \sqrt{2}\left(\sin ^{2} A-\sin ^{2} C\right) = (a-b) \sin B,\] 
and the circumradius 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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