Two circles of radius 1 are centered at $(4,0)$ and $(-4,0).$ How many circles are tangent to both of the given circles and also pass through the point $(0,5)$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Two circles of radius 1 are centered at $(4,0)$ and $(-4,0).$ How many circles are tangent to both of the given circles and also pass through the point $(0,5)$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Two circles of radius 1 are centered at $(4,0)$ and $(-4,0).$ How many circles are tangent to both of the given circles and also pass through the point $(0,5)$?
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