A common failure in prioritization is to only work on the highest priority task.
Consider eating and drinking. You need to eat and drink water to stay alive. You need to drink more often than you eat. Therefore, drinking is the highest priority.
It would clearly be incorrect to only eat before you starve. Yet, we often approach prioritization decisions as if it were optimal to always drink water and to only eat every few weeks right before you would die.
"Do both" is an annoying thing to hear from someone you work with, but it's also honest.
If you have to choose, drink water. Otherwise don't forget to eat.