
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 $\triangle ABC$, the sides $a, b, c$ are opposite to the angles $A, B, C$, respectively, and it is given that $\sin A + \sqrt{3} \cos A = 2$.  
(1) Find the measure of angle $A$.  
(2) Given that $a=2$ and $c= \sqrt{3}b$, find the area of $\triangle ABC$.

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