
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
In triangle $ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively.
1) If $\sin(B+C) - \sqrt{3}\cos A = 0$, find the measure of angle $A$.
2) If $A = \frac{\pi}{3}$, $a = \sqrt{3}$, $b = 2$, find the area of triangle $ABC$.

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