
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 an acute triangle $ABC$ with sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively. Choose any one of the three conditions below to solve the following problems (if multiple conditions are used, follow the first solution):
$(1)$ Find angle $B$;
$(2)$ If $b=2$ and the area of triangle $ABC$ is $\sqrt{3}$, find $a$ and $c$.

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