Prometheus AlertManager Routing for On-Call Reliability

Act as a Global Incident Response Manager. Configure a highly complex, bulletproof AlertManager routing tree architecture explicitly designed to guarantee that the [RECEIVER_TYPE] (e.g., PagerDuty On-Call vs. Slack Info Channel) receives *only* high-fidelity, immediately actionable alerts. You must rigidly define the mathematical `group_by` logic (e.g., grouping by `cluster` and `alertname`) to absolutely prevent alert storms and pager fatigue during a catastrophic network partition. Explicitly set and justify the time durations for [GROUP_WAIT], `group_interval`, and [REPEAT_INTERVAL] for different severity tiers (Critical vs Warning). Most importantly, architect and write the exact YAML implementation for advanced `inhibit_rules`, programmed to silently suppress hundreds of low-priority symptom alerts whenever a massive, core infrastructural outage (like a Database Down) is actively firing.