tenant broke lease

My tenant bought a house and want to vacate the house end of this month, he only gave me 1 month notice. Our 1 year lease ends April next year. My thought is:
1)put advertise to find a new tenant as soon as possible
2)require tenant pay rent until a new tenant moves in
3)require tenant pay all advertise costs

Is it OK? If we can not resolve the issue, what legal steps I can take?