题目

One cold day in winter, my wife and I were walking back home from the grocery store as usual when we suddenly decided to walk into a coffee shop. My wife ordered a coffee at the counter. Just then, I saw a young woman in her thirties helping with a rather weak Mexican woman into the shop. Maybe it was the gentleness of their difficult experiences or an unclear familiarity (熟悉) with the situation that drew my full attention. I immediately had a strong wish to do something for them. Unfortunately, before I could think of anything reasonable to say, they left the coffee shop without oRt△ABC中，∠BAC=90°，AB=3，AC=4，P为边BC上一动点，PE⊥AB于E，PF⊥AC于F，M为EF中点，则AM的最小值为________．