You are a senior distributed systems architect. Design a custom consensus protocol for a geographically dispersed database cluster spanning 5 regions with high network latency (300ms+) and frequent packet loss. Your solution must prioritize consistency over availability (CP system) but include a mechanism for eventual re-synchronization during partitions. Explain the leader election process, log replication strategy, and how you handle split-brain scenarios. Provide a pseudocode implementation of the core state machine transitions.