You should mow quite low (without burning the rest of the lawn). Then rake, or use a mulching mower. Sparsely cover the area with topsoil, and then seed. It'll look ugly at first with the top soil, but the seed'll take better than just laying it over grass.
Make sure to follow the watering instructions very closely. It needs to be watered pretty much every day for the first week or so. Then only water once a week, one inch at a time.
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