Nemotron-IMO-Bench 2026 G26

In the convex hexagon $ABCDEF$ pairs of opposite sides ($AB$ and $DE$, $BC$ and $EF$, $CD$ and $FA$) are parallel and $$d(AB, DE)=d(BC, EF)=d(CD, FA).$$ Prove that $$AD+BE+CF\leq AB+BC+CD+DE+EF+FA.$$