Let $P$ be a point on the curve $xyz^2 = 2$ in three-dimensional space.  Find the minimum distance between $P$ and the origin.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $P$ be a point on the curve $xyz^2 = 2$ in three-dimensional space.  Find the minimum distance between $P$ and the origin.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
Let $P$ be a point on the curve $xyz^2 = 2$ in three-dimensional space.  Find the minimum distance between $P$ and the origin.
train