HPA and VPA thrashing

An internal API runs on Kubernetes with both a HorizontalPodAutoscaler (target 60% CPU, 4-30 pods) and a VerticalPodAutoscaler in Auto mode that resizes pod CPU/memory requests. Since both were enabled last week, the deployment thrashes: pods are evicted and recreated every few minutes, replica count swings, and p99 has a jagged saw-tooth. kubectl get events is full of VPA evictions and HPA scale events interleaved. Each control loop on its own looked fine in staging. How do you triage and stabilize this?