Question 71: Positive real numbers $x, y$ satisfy the following conditions: there exist $a \in[0, x], b \in[0, y]$, such that $a^{2}+y^{2}=2$, $b^{2}+x^{2}=1, a x+b y=1$, then the maximum value of $x+y$ is $\qquad$ _.