Let $\vec{r}=\sin x(\vec{a} \times \vec{b})+\cos y(\vec{b} \times \vec{c})+2(\vec{c} \times \vec{a})$ ，where $\vec{a}, \vec{b}$ and $\vec{c}$ are three non－coplanar vectors． It is given that $\vec{r}$ is perpendicular to $(\vec{a}+\vec{b}+\vec{c})$ ．Then the possible value（s）of $\left(x^2+y^2\right)$ is／are