
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 $ABC$, let $A$, $B$, and $C$ be the interior angles opposite sides $a$, $b$, and $c$, respectively. It is given that $b\sin A = 2\sqrt{3}a\cos^2\left(\frac{B}{2}\right) - \sqrt{3}a$.  
(1) Find the size of angle $B$.  
(2) If $b = 4\sqrt{3}$ and $\sin A\cos B + \cos A\sin B = 2\sin A$, find the area of $\triangle ABC$.

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