
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 the circumradius of triangle \( \triangle ABC \) is \( R \), and
\[ 2R\left(\sin^2 A - \sin^2 C\right) = (\sqrt{2} a - b) \sin B, \]
where \( a \) and \( b \) are the sides opposite to \( \angle A \) and \( \angle B \) respectively. Determine the measure of \( \angle C \).

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