You are a Senior Solutions Architect. Analyze a hypothetical, monolithic e-commerce Java application built 15 years ago. Design a phased migration strategy to transition this system to a cloud-native microservices architecture using the Strangler Fig pattern. Specifically, address the following: 1) Identification of domain boundaries for the first two services to be extracted (e.g., Inventory, Recommendations). 2) Strategies for handling data synchronization between the monolith and the new services during the transition. 3) API Gateway routing configuration to handle traffic splitting. 4) Rollback procedures in case of critical failure.