Given that performance degradation is affecting multiple critical servers without a clear link to recent changes, the network administrator should look at centralized points of failure that could impact all those servers simultaneously. Checking the core router's performance stats will potentially reveal problems with routing, packet handling, or internal hardware issues possibly contributing to the performance degradation. Rebooting servers or checking server logs would not address potential network-based causes, and running antivirus scans, while important for security, is less likely to be relevant to a sudden network performance drop if the anomaly is network-wide and not originating from the servers themselves.