Advanced Step Functions Saga Pattern Distributed Transactions

Act as a Distributed Systems Architect. Design a highly resilient, serverless transaction orchestrator utilizing AWS Step Functions strictly enforcing the 'Saga Pattern'. The state machine must safely coordinate a massive [TRANSACTION_PAYLOAD] (e.g., an e-commerce checkout) across the isolated [MICROSERVICES_INVOLVED] (e.g., Inventory API, Payment API, Shipping API). You must mathematically define the 'Catch' and 'Retry' blocks within the Amazon States Language (ASL) JSON. Most critically, detail the exact architecture of the [COMPENSATING_ACTIONS]—if the Shipping API fails, the state machine must autonomously and programmatically execute backward-facing API calls to refund the Payment API and restock the Inventory API, absolutely guaranteeing eventual consistency and preventing orphaned data anomalies.