Analyze a complex SQL query involving five table joins (including many-to-many relationships) running on a multi-terabyte PostgreSQL database. The current execution time is over 10 minutes. Propose specific indexing strategies (e.g., covering indexes, partial indexes, BRIN indexes), query rewriting techniques (e.g., CTEs vs subqueries, avoiding functions in WHERE clauses), and schema optimizations (e.g., denormalization, partitioning). Explain how you would use the EXPLAIN ANALYZE output to validate your changes.