" No! " said Harry indignantly, racking his brains to think what he could have done that would make Snape pursue him to Grimmauld Place. Had his last piece of homework perhaps earned a 'T'?
The focused mode is where you're racking your brain trying to use your focused awareness to figure something out, whether it be a math problem or what's going on in a TV show in a foreign language.
" I thought he was! " said Harry, racking his brains to remember when Dumbledore had told him this, but now that he came to think of it, he was unable to recall Dumbledore ever telling him what Slughorn would be teaching.