How can I (24F) get my ADD husband (25M) to share more of the mental chore load?

We've been together for 4 years, living together for 3. We were living in an apartment, but we've recently ought a house and have doubled our choreload and are still unpacking and stuff.
My husband is not lazy, bit he has a hard time seeing what needs to be done and starting tasks. For example, large cardboard trash like pizza boxes do not get thrown away (they go in recycling outside instead of in the trash inside) and they do not get thrown away until I ask. Kitchen does not get cleaned until I ask. I do my chores every Saturday morning, and if he can start his chores while I do mine, we're good, but if not, I'll have to nag him to do chores Sunday night. If people are coming over though, he'll deep clean the place in a heart beat. He also struggles more with tasks that he cannot "see". Ex, hell sweep the living room weekly because it gets dirty but not so much our bedroom, which can go months between sweeps. He never missed any of the floor when we had carpet.
It's also his job to refill the pets water, and I have to point out that the water is getting low before he'll do so. They have multiple water bowls throughout the house, so its not like they don't have water access when one is empty.
Dating.mobi, any advice?
Tldr: I need advise on how to navigate chores with my add husband.


Source.