Title pretty much says it. Do workers at a distribution post pick up goods from storages to transport to drop-off points directly, or can they only transport goods already in the post? In the latter case, can they move things from storages to the post themselves, or do I need haulers as well?

I've seen some old posts say they can not, but I've also seen a dev diary that says they can, so I'm a bit confused.

EDIT: Thanks so much for all the replies, everyone! It really helps a lot. I'm already using haulers, but they tend to be very busy, so I was worried I'd have to build it very close to storages, but if the post workers themselves can do that part, half-way, like Shivatis suggested, is probably best. Thank you all for the swift replies :)