Tenant lease break situation and re-renting advice

[Jeff Bridges]

I have a tenant with a lease ending July 31 and is breaking their lease to move somehwhere else instead of wait out the end of their lease. They just moved out early this past saturday .They've been there for 10 years. I explained they are on the hook for the full lease until the unit is re-rented. I've agreed to list it and get cooperation from tenant with showings and pointed out that feb is a slower month to get interest in applicants and that they would be on the hook for additional rent if I couldnt rent it by Feb 1. I've had several showings in jan and one applied, qualified and was approved for Early feb move in. New applicant now says shes available to move in March 1 and not feb 10 as she originally indicated.  If I accepted this new move-in date, I would use current tenants deposit to pay the feb rent. What are my obligations here? It's looking less likely I'll be able to do more showings and result in someone moving in Feb 1 at this point and I already dedicated alot of time grinding out pre-qualifying and coordinating showings in January. The easiest thing is to accept a march 1 move in and forfeit the existing tenants deposit, resulting in no out of pocket to me, but I also know I need to attempt to re-market for rent as quickly as possible, but it seems like I did that already, but just making sure I dont need to keep it listed when I can have this applicant put down a deposit ASAP which she has agreed to. Another thing I can do is try to compromise with the new applicant and see if they will consider a Feb 15 lease start date to hold the unit until they can move in march 1, but again its not my money since the deposit covers the month anyway. So I'd only be getting half the deposit back to the tenant off the back of the new tenant who really wants march 1. My gut says accept march 1 move in and existing tenant forfeits deposit to cover month of feb that was not rented out. Thoughts appreciated!