Let $a,b,c,d\in \mathbb{R}$ and $\left\{\begin{matrix} 0<a\leq b\leq c\leq d\\ \frac{1}{a}+\frac{2}{b}+\frac{d}{c}\geq 3\\ \frac{2}{b}+\frac{d}{c}\geq 2 \end{matrix}\right.$. Prove that:
$$a^4+b^4+c^4-d^4\leq 17$$