Expectation of the maximum of two correlated standard normal variables squared

Question

Assume we have two random variables X and Y. They are joint Gaussian with mean 0 and standard deviation 1 and correlation $\rho$.

1. What is $E[max\{X^2, Y^2\}]$
2. What is $E[max\{X,Y\}^2]$

I know that when X and Y are independent, $P\{max\{X,Y\}<m\} = P\{X<m\}*P\{Y<m\}$. Also $X^2$ is a Chi-square random variable. But I am having trouble to use this equation when X and Y are not independent.