
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
Given in $\Delta ABC$, the angles $A$, $B$, and $C$ are opposite to the sides $a$, $b$, and $c$ respectively, and it is known that $a\sin C=\sqrt{3}c\cos A$.

$(1)$ Find angle $A$;

$(2)$ If $b=2$ and the area of $\Delta ABC$ is $\sqrt{3}$, find $a$.

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