reseed thin grass 3pt? no clue

Just got my 1st tractor, big oliver 98pto horse w/ 3pt. We had some old terraces bulldozed a year ago, and then seeded by a fellow (I wasn't there, don't know what he used). Just cut down all weeds and sunflowers with flail mower today (clippings are thick here and there, grass and weed stalks about 6-12 inches tall now). Have some thin areas that have some new grass, but they need more seed. I would like to reseed a bit, but without tearing up existing established grass. Haven't a clue, what to use, or what to call it. Can anything imbed a seed a bit, but not tear up existing grass, and not clog on the weed and grass cuttings?

Any suggestions? would like to know what to look for at an auction, has to be cheap. pull or 3pt, I don't care. As long as it works better than a garden rake and seeding by hand.

Thank You!

casey in SD