You are tasked with migrating a 10-year-old monolithic e-commerce application written in Java (Spring MVC) to a microservices architecture. The monolith contains a tightly coupled inventory, payment, and user management module. Outline a step-by-step strangler fig pattern strategy for this migration. Specifically, explain how you would: 1) Identify bounded contexts for the new services. 2) Establish data synchronization patterns during the transition phase. 3) Handle distributed transactions to ensure data consistency between the old monolith and new services. 4) Implement API gateways to route traffic. Provide pseudo-code or architectural diagrams describing the interface segregation contracts.