
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$ respectively. It is known that $b\sin A = \sqrt{3}a\cos B$.  
$(1)$ Find the measure of angle $B$.  
$(2)$ Choose one of the following conditions as known from conditions ①, ②, and ③, such that triangle $\triangle ABC$ exists and is uniquely determined, and find the area of $\triangle ABC$.  
Condition ①: $a=4$, $b=3$;  
Condition ②: $c-a=1$, $b=\sqrt{7}$;  
Condition ③: $c=3$, $\cos C=\frac{{\sqrt{7}}}{{14}}$.  
Note: If multiple conditions are chosen and solved separately, the first solution will be scored.

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