Customer Cohort Segmentation

Write a SQL query to segment customers into new, returning, and churned users based on their activity dates.

Use the activity period from 2025-01-01 through 2025-01-31. A new customer first became active during this period, a returning customer was active during the period and had earlier activity, and a churned customer had no activity during the period but last activity on or before 2024-12-01.

Output

1. Return one row per classified customer with customer_id, segment, first_activity_date, and last_activity_date.
2. Exclude customers who do not meet one of the three definitions.
3. Order by segment as new, returning, churned, then by customer_id.