
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 three conditions from the following equations:①$a\sin C=\sqrt{3}c\cos A$, ②$b^{2}+c^{2}-a^{2}=bc$, ③$\sqrt{3}\sin A-\cos A=1$, and supplement it in the question below, then solve.<br/>Question: Given that $a$, $b$, $c$ are the three sides opposite to the internal angles $A$, $B$, $C$ of triangle $\triangle ABC$, and ____,<br/>$(1)$ find $A$;<br/>$(2)$ if $a=2$, then the area of $\triangle ABC$ is $\sqrt{3}$, find $b$ and $c$.<br/>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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