Comp. value in 2 columns against a list and disp. text in 3r

Hello,

I need some help as I cant figure out how to construct this. I have been using a combination of IFS, AND, & VLOOKUP functions but I cant seem to figure out how to hit all the conditions i need.

I have specific values in 2 different columns that I need to compare against a list output a specific word against.

List A B
123 123 123
325 456 456
258 789 719
123 258
719 101
909


1. If the value in A is the same as the value in B text should be "local"
2. If the value in A is on the list and the value in B is not then text should be "remote"
3. If the value in B is on the list and the value in A is not then text should be "assigned"
4. if the value in A is blank but the value in B is on the list then text should be "available"
5. if the value in A is on the list but the value in B is not the text should be "vacant"
6. If the value in A and B are on the list but not the same values then the text should be "crossed"

Thanks in advanced. I have been trying to figure this out for 3 days.