Let $P$ be a point on the graph of the equation $xyz = 1$ in three-dimensional space.  Find the minimum possible 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 graph of the equation $xyz = 1$ in three-dimensional space.  Find the minimum possible distance between $P$ and the origin.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{3}
Let $P$ be a point on the graph of the equation $xyz = 1$ in three-dimensional space.  Find the minimum possible distance between $P$ and the origin.
train