IMO 2020 — Complete Shortlist Question 4

Let $a, b, c, d$ be four real numbers such that $a \geqslant b \geqslant c \geqslant d\gt 0$ and $a+b+c+d=1$. Prove that

$$
(a+2 b+3 c+4 d) a^{a} b^{b} c^{c} d^{d}\lt 1
$$