HMMT 2013 A8

Let $x, y$ be complex numbers such that $\frac{x^{2}+y^{2}}{x+y}=4$ and $\frac{x^{4}+y^{4}}{x^{3}+y^{3}}=2$. Find all possible values of $\frac{x^{6}+y^{6}}{x^{5}+y^{5}}$.