
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 triangle $ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$. Also, $b = \frac{2\sqrt{3}}{3}a \sin B$ and $A$ is an acute angle.
1. If $a = 3$ and $b = \sqrt{6}$, find angle $B$.
2. If the area of triangle $ABC$ is $\frac{\sqrt{3}}{2}$, $b + c = 3$, and $b > c$, find $b$ and $c$.

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