
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 $ABC$, the sides opposite angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively. The radius of the circumcircle is 1, and it satisfies $2(\sin^2 A - \sin^2 C) = (\sqrt{2}a - b)\sin B$.
(Ⅰ) Find the measure of angle $C$.
(Ⅱ) Find the maximum area of triangle $ABC$.

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