
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
Let the sides opposite to the angles $A$, $B$, $C$ in triangle $ABC$ be $a$, $b$, $c$ respectively, and $b= \frac{2 \sqrt{3}}{3}a\sin B$, with angle $A$ being acute.

$(1)$ If $a=3$ and $b= \sqrt{6}$, find the angle $B$;

$(2)$ If the area of $\triangle ABC$ is $\frac{ \sqrt{3}}{2}$ and $b+c=3$ with $b > c$, find $b$ and $c$.

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