
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 opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. The vector $\overrightarrow{m} = (b, -\sqrt{3}a)$ is perpendicular to the vector $\overrightarrow{n} = (\cos A, \sin B)$.  
(1) Find $A$;  
(2) If $B + \frac{\pi}{12} = A$, and $a=2$, find the area of $\triangle ABC$.

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