SAT1000 - P548

Given that $x,y \in \mathbb R$ and $x^2+y^2 \leq 1$ , find the minimum value of $|2x+y-2|+|6-x-3y|$ .

Let $M$ be the minimum value. Submit $\lfloor 1000M \rfloor$ .

Have a look at my problem set: SAT 1000 problems