
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
Let $\triangle ABC$ have sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$, respectively, and $(\sin B - \sin C)(b + c) = (\sin A - \sqrt{2}\sin C)a$.  
$(1)$ Find the measure of angle $B$.  
$(2)$ If $b = \sqrt{2}$ and the perimeter of $\triangle ABC$ is $2 + 2\sqrt{2}$, find the area of $\triangle ABC$.

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