Conversation so far:
What was the Count's big break?
Basie gained his first steady job at Leroy's, a place known for its piano players and its "cutting contests..
Did Leroy's lead to other opportunities?
Willie "the Lion" Smith helped Basie out during the lean times by arranging gigs at "house-rent parties.
Whose parties did the Count play at?
CANNOTANSWER.
After the parties, what did the Count do for work?
In 1928, Basie was in Tulsa and heard Walter Page and his Famous Blue Devils, one of the first big bands, which featured Jimmy Rushing on vocals.

Question: Did Basie get involved with Walter Page's band?
Self-contained rewrite: Did Basie get involved with Walter Page's band?