Tenant vanished - do I need to evict before re-renting?

[Samuel Rinaldo]

One of my tenants didn't pay rent on time so I went to get in touch with her and her phone is off.  All payments before were on time. I sent someone to serve the 3 day notice and he let me know that the unit looked vacant. So I go check the unit out and sure enough it was empty, the tenant even cleaned the house really well before leaving. The tenants in the neighboring units haven't seen them in a couple weeks. She did not leave the key behind.  About 8 months remaining on the lease.

My lease does not cover abandonment which I now realize should be included. So now that I've served the 3 day "pay or quit" notice properly can I proceed as if she took the "quit" option and legally change the locks and re-rent the house? Or do I need to proceed with the full eviction process even though this tenant is long gone? 

I have a deposit equal to two months rent.

This is in upstate NY.