You discard, put counters, and draw all while Nantuko Cultivator's ability is resolving. Nothing can happen between the three, and no player may choose to take actions.
14-06-2019
wotc
If an effect modifies how many +1/+1 counters you put on Nantuko Cultivator, the number of cards you draw isn't modified. Likewise, if an effect modifies how many cards you draw, the number of +1/+1 counters you put on Nantuko Cultivator won't be modified.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.