A super hard inequality to be shown

[vocal obsidian]

$x$ and $y$ are two real numbers such that: $1 \leq x^2 + y^2 - xy \leq 2$ Show that: $\frac{2}{9} \leq x^4 + y^4 \leq 8$
I was given this as a middle school student so it should be solvable using some basic math,any help is really appreciated