Let $x$ and $y$ be real numbers satisfying
\[\frac{2}{x} = \frac{y}{3} = \frac{x}{y}.\]Determine $x^3.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be real numbers satisfying
\[\frac{2}{x} = \frac{y}{3} = \frac{x}{y}.\]Determine $x^3.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
Let $x$ and $y$ be real numbers satisfying
\[\frac{2}{x} = \frac{y}{3} = \frac{x}{y}.\]Determine $x^3.$
train