Say I have a sensei's divining top out, and I want the card on the top of my deck, but I don't want to draw top next turn. Can I do the following:

1. Activate top to look at the top 3 cards and put that ability on the stack?
2. Use top's tap and draw a card ability and put that on the stack.
3. Begin resolving the stack by first drawing a card and putting the top on top.
4. Finish resolving the stack by reordering my top 3 cards?

I have never seen this done so I have a feeling something is illegal here.