
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 $\triangle ABC$, $b^{2}+c^{2}=a^{2}+\sqrt{3}bc$.  
$(Ⅰ)$ Find the measure of $\angle A$;  
$(Ⅱ)$ Among the following three sets of conditions, there is exactly one set that makes the triangle exist and uniquely determined. Identify that set of conditions and find the area of $\triangle ABC$.  
Condition ①: $\sin B=\frac{\sqrt{2}}{2}$, $b=\sqrt{2}$;  
Condition ②: $\cos B=\frac{2\sqrt{2}}{3}$, $a=\sqrt{2}$;  
Condition ③: $a=1$, $b=\sqrt{2}$.

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