Table schema:
CREATE TABLE table_name_29 (average INTEGER, interview VARCHAR, state VARCHAR, swimsuit VARCHAR, evening_gown VARCHAR)

Question: What's the lowest average for a swimsuit over 6.89, evening gown over 7.76, and an interview over 8.57 in illinois?
SQL: SELECT MIN(average) FROM table_name_29 WHERE swimsuit > 6.89 AND evening_gown > 7.76 AND state = "illinois" AND interview > 8.57