When do I add the red potatoes and carrots when making corned beef and cabbage in the crock pot?

I planned on putting the corned beef in the crock pot with beef broth and cooking it on low for about 8 hours but I'm not sure when to add the red potatoes and carrots. I'm worried that If I put them in with the beef they will get too soft, but if I put them in too late they will be too hard. This is my first time making corned beef and cabbage. I planned on adding the cabbage at the end, durring the last hour? Any suggestions?