
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 in $\triangle ABC$, the sides opposite angles A, B, and C are denoted as $a$, $b$, and $c$ respectively, and it is known that $b^2 = a^2 + c^2 - \sqrt{3}ac$ and $c = \sqrt{3}b$.  
(1) Find angle A;  
(2) If the radius of the circumcircle of $\triangle ABC$ is 2, find the area of $\triangle ABC$.

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