
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
Choose one of the following conditions:①$asinB-\sqrt{3}bcosA=0$；②$\left(\sin B-\sin C\right)^{2}=\sin ^{2}A-\sin B\sin C$；③$2\cos A\left(c\cos B+b\cos C\right)=a$. Then, complete the blank line below and solve the problem. Problem: In triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$, respectively, and satisfy _____.<br/>$(1)$ Find $A$;<br/>$(2)$ If $a=\sqrt{3}$ and $\sin C=2\sin B$, find the area of $\triangle ABC$. Note: If multiple conditions are chosen to solve separately, the first answer will be graded.

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