Thatch is an accumulation of organic matter just above the soil surface which can prevent water and nutrients passing through. At the moment you have just removed all the green growth leaving the brown stems behind. You goal should be to remove as much of the stem growth as possible. This will promote new growth very close to the soil level where you can cut and use the groomer regularly to reduce lateral stem growth. Don't wait for it to green up. Just smash it now.

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You can do that with a combination of the groomer, the reel and the rotary mower. My rotary gets used to do the bulk of the cutting this time of year and it also does a great job of sucking up all the debris that gets brought up.