First, do the things for yourself, not for your partner. For example:
(I) you iron your clothes only, not his;only;
(II) you send only your clothes only for laundry;
(III) you order just your delivery food;
(IV) you buy only your stuff in the supermarket, not his.
This way, heyour partner will need to do most of the same work for himself, not necessarily at histhe same pace. HeYour partner is going to be punished by histheir own procrastination.
But this still comes with a problem: if you share a bed, you can't make only half-bed; you can't take only your trash outside, as the smell would still be a problem; the sink will still be full of dirty plates if you wash only yours; you can't pay half of the bill if heyour partner won't pay histhe other half... and so on.
There are activities that need to be done completely. So, you divide these specific tasks - the urgent ones are hisassigned to your partner, the less urgent are yours. Some examples:
(a) One is responsible for buyings things; the other for arranging them in the house. As buying things are more urgent, this should be hisa task assigned to your partner. You say he needs to buy: "The toilet paper NOWneeds to be bought NOW".
(b) The last to get out of bed is the one who will make the bed. If heyour partner gets up before you, than ok, you just make the bed. If it is the other way around, you force him to makeyour partner makes the bed. If not, how could you sit on the bed to study? You need to make the bed NOW.
(c) If you are blocked by one of hisyour partner tasks, this task is urgent. The sink is full of dirty dishes and you want to cook - he needsthey need to wash thembe washed NOW, so you can get enough room. This can't wait, or dinner is going to be cancelled and heyour partner would pay for the food delivery.
You can get creative here - the most efficient thing for procrastinators are dealing with urgent things. When something is urgent, he needsthey need to do it NOW. Less urgent things are the problem, and you should take these tasks for yourself if you want to avoid conflicts.