Find the minimum possible value of the largest of $xy$, $1-x-y+xy$, and $x+y-2xy$ if $0\leq x \leq y \leq 1$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the minimum possible value of the largest of $xy$, $1-x-y+xy$, and $x+y-2xy$ if $0\leq x \leq y \leq 1$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{4}{9}
Find the minimum possible value of the largest of $xy$, $1-x-y+xy$, and $x+y-2xy$ if $0\leq x \leq y \leq 1$.
train