What is the most logical next event?

How to know if your lawn needs dethatching
Walk on the lawn to see if it feels firm or spongy.
The first thing that gives you a hint at whether or not your lawn needs to be dethatched is the feel of it. Walk around for awhile and see if the ground feels firm.
If it feels spongy, or almost bouncy, that's a sign that the thatch has gotten too thick. If you don't mind the feeling, walk around barefoot to get an even better feel of the firmness of the ground.