As far as informing the headmaster, Harry had no idea where Dumbledore went during the summer holidays. He amused himself for a moment, picturing Dumbledore, with his long silver beard, full-length wizard's robes, and pointed hat, stretched out on a beach somewhere, rubbing suntan lotion onto his long crooked nose.
As far as executing work is concerned, you do it all in order. You do it in contractual order. There's no overlap, it's just continuation of your ordinary work. You move from one project into another.