Detect sessions and gaps using SQL LEAD

Write a single ANSI-SQL query that (a) assigns per-user session_ids when the gap between consecutive events exceeds 30 minutes, (b) computes session_start, session_end, event_count, session_length_seconds, and next_session_gap_seconds (time from this session_end to the next session_start for the same user), and (c) uses window functions including LEAD at least once. Schema:

• events(user_id INT, ts TIMESTAMP, action VARCHAR) Sample data: +---------+---------------------+---------+ | user_id | ts | action | +---------+---------------------+---------+ | 1 | 2025-08-01 09:00:00 | view | | 1 | 2025-08-01 09:10:00 | click | | 1 | 2025-08-01 10:00:00 | view | | 2 | 2025-08-01 12:00:00 | view | | 2 | 2025-08-01 12:20:00 | click | | 2 | 2025-08-01 12:45:00 | purchase| | 2 | 2025-08-01 14:00:00 | view | +---------+---------------------+---------+ Requirements:
• Use LAG to detect new sessions and a running SUM to form session_ids per user.
• Use LEAD(ts) to compute next_event_ts and derive next_session_gap_seconds.
• Return columns: user_id, session_id, session_start, session_end, event_count, session_length_seconds, next_session_gap_seconds (NULL if no next session).