
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 a triangle $\triangle ABC$ with angles $A$, $B$, $C$ and their corresponding sides $a$, $b$, $c$. It is known that $\frac{a+b}{\sin(A+B)} = \frac{a-c}{\sin A - \sin B}$ and $b=3$.

1. Find angle $B$;
2. If $\sin A = \frac{\sqrt{3}}{3}$, find the area of $\triangle ABC$.

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