Three mutually tangent spheres of radius 1 rest on a horizontal plane.  A sphere of radius 2 rests on them.  What is the distance from the plane to the top of the larger sphere?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Three mutually tangent spheres of radius 1 rest on a horizontal plane.  A sphere of radius 2 rests on them.  What is the distance from the plane to the top of the larger sphere?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3+ \frac{\sqrt{69}}{3}
Three mutually tangent spheres of radius 1 rest on a horizontal plane.  A sphere of radius 2 rests on them.  What is the distance from the plane to the top of the larger sphere?
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