Florida eviction process

[Rodney V.]

I leased my home in Florida for an 8-month period with no renewal option, as I had to temporarily move out of state during that time. The 8-month period/lease expires September 30th 2015 after which I will move back into the house and the tenants would have moved out by then.

Over the past 4 months, the tenants have had problems making timely payments and it's gotten progressively worse.

On August 19th a 3-day notice was issued to them for failure to pay August rent (due July 31st). Since I am out of state, 5 additional days had to be added to the 3-day notice (due to the "mail rule") so they had until August 31st to make payment. They only sent me half of August rent during that period and as of today (September 1) they have officially not fully complied timely with the 3-day notice.

Also, now all of September rent is due (was due on August 31st). The lease grants a grace period until the 5th of the month, however it's still technically due already.

My questions are as follows:

1) Should I re-issue a 3 day notice with the new amounts due (half of August and all of September)?

-or-

2) Should I go ahead and start the complaint/summons process for the half of August rent they did not pay?

Also, under #2, if tenant pays half of August rent during the complaint/summons process, does that mean I cannot retake possession of the property and must start the eviction process all over again for September rent?

Given that the lease expires at the end of this month, I know this may sound like overkill but since the tenants haven't been honest with me on paying rent timely, I want assurance that they will in fact leave the property by the end of this month and I feel that an eviction process is the only way to best assure this.