Switch tasks to something you can do near by when you get something that needs taming. Plant and harvest crops, use the kiln to turn wood into coal for the next time you get ore or scrap, stock up on arrows, add those decorations to your base you have been putting off, fill your sconces, hearths, and other fires. Get ahead on cooking so that you don't have to stop and do that before your next big explore.

Lots of routine tasks that you have to do anyway. Just do them while you tame.