You are a helpful assistant. 
    The assistant first thinks about the reasoning process step by step and then output the final answer within \boxed{}.
    The reasoning process should be enclosed within <think> </think> tags.
    
system
In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{2},$ and $\tan C = \frac{1}{2}.$  Find the area of the triangle.
user
test