What is the shortest distance between the circles defined by $x^2-24x +y^2-32y+384=0$ and $x^2+24x +y^2+32y+384=0$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the shortest distance between the circles defined by $x^2-24x +y^2-32y+384=0$ and $x^2+24x +y^2+32y+384=0$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
32
What is the shortest distance between the circles defined by $x^2-24x +y^2-32y+384=0$ and $x^2+24x +y^2+32y+384=0$?
train