
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 a circle of unit radius, $\triangle ABC$ is inscribed with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively. Given the equation $2(\sin^2 A - \sin^2 C) = (\sqrt{2}a - b)\sin B$,

(1) Find the measure of angle $C$;

(2) Find the maximum area of $\triangle ABC$.

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