Design a system for managing versioning and backward compatibility of APIs in a distributed system. The system should allow for the introduction of new features, changes, and improvements to APIs without breaking existing client integrations. Consider factors such as versioning strategies, API documentation, deprecation policies, and communication mechanisms in your design. Discuss how you would version APIs using URL paths, request headers, or other mechanisms, and how you would handle backward compatibility for existing clients. Additionally, address how you would communicate API changes to developers, provide migration guides, and manage deprecated endpoints. Provide insights into the technologies, tools, and best practices you would employ to implement this versioning and backward compatibility system effectively.