SILK-ROAD 2015 Problem 1

Prove that there is no positive real numbers $a,b,c,d$ such that both of the following equations hold. $$\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=6 , \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}=32$$ .