You are a Senior Solutions Architect. Analyze a hypothetical e-commerce monolith containing Order Management, Inventory, and User Profile modules within a single codebase sharing a database. Design a migration strategy to decompose this into distinct microservices. Specifically, address: 1) How to define Bounded Contexts for each service. 2) Strategies for handling data consistency when the ACID transactions are split across services (e.g., Sagas). 3) API Gateway patterns for routing. 4) Handling shared libraries or common utility code. Do not provide code; focus on architectural diagrams, data flow, and infrastructure considerations.