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
Four circles with radii 1, 2, 3, and $r$ are externally tangent to one another, where $r$ is the smallest radius.  Compute $r$.
user
test