inequality with the $\frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}\ge\frac{a+b+c+d}{\sqrt[4]{abcd}}$

Question

Let $a,b,c,d$ be side of quadrilateral $ABCD$,prove or disprove

$$\dfrac{b}{a}+\dfrac{c}{b}+\dfrac{d}{c}+\dfrac{a}{d}\ge\dfrac{a+b+c+d}{\sqrt[4]{abcd}}$$