Design a metrics and logging service.

Focus on the core functionalities that a metrics and logging service should provide. Start by identifying the types of metrics and logs that are essential for various stakeholders, such as performance metrics, error logs, and user activity logs. Consider the architecture of the service, including data ingestion, storage, and retrieval mechanisms. Discuss how you would ensure scalability, reliability, and real-time processing of data. Finally, address how you would implement monitoring and alerting features to proactively manage system health and performance.