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I've submitted the institutions I attended. Do I have to do anything else, or will CAS request transcripts for me?

Also, how long does it generally take for CAS to compile a report (I attended two institutions -- a CC, and a 4year university)?

Enter all your institutions attended in LSAC.
Print out the transcript form that LSAC generates for each school.
Include LSAC's form with your transcript request to each school. The schools must include the form when they send your transcripts directly to LSAC (NOT to you).
Once LSAC has all your transcripts, I think it takes a couple of days to generate a report.