Let $\displaystyle a,b,c,d\in \mathbb{R}$ and $\displaystyle \left\{\begin{matrix}

0<a\leq b\leq c\leq d\\

\frac{1}{a}+\frac{2}{b}+\frac{d}{c}\geq 3\\

\frac{2}{b}+\frac{d}{c}\geq 2

\end{matrix}\right.$. Prove that:

$\displaystyle a^4+b^4+c^4-d^4\leq 17$