You are tasked with migrating a 10-year-old monolithic e-commerce Java application to microservices without halting development. Draft a step-by-step migration plan employing the Strangler Fig pattern. Your plan should identify: 1. A specific bounded context (e.g., 'Inventory Management') to extract first. 2. How to set up a proxy or API Gateway to route traffic between the old monolith and the new service. 3. Strategies for data synchronization and dual-write scenarios during the transition period. 4. A rollback strategy in case the new service fails in production.