work & live

Are they state or action verbs? Or both?

thanks in advance

My references say that state verbs are not used in the continuous tense. Both of these verbs are often used in continuous tense, so I do not think they can be state verbs: “I am living in Nashville now. I am working hard every day.”

English Result book says live and work are state verbs,

[color=blue](usage of would and used to)
it explains :

use [color=blue]would to describe repeated action in the past, but not a state.
use [color=blue]used to to describe a state or repeated action in the past.

I used to live in Italy. [color=green]Correct
I would live in Italy. [color=red]Incorrect

but as you mentioned, they can be used in continuous tenses.