Charging Tenant Extra Rent for Not Providing Notice Question

Took over new property which was on a different management companies lease. We mailed/ emailed a renewal offer around 73 days prior to the lease ending (we try to send these out 90 days prior but got delayed since we just took it over). The tenant gave us notice 45 days prior to the lease ending that they are planning to vacate. The property owner wants to charge them an extra months rent because they did not give 60 days notice. 

The lease states "This lease contract will automatically renew month-to-month unless either party gives at least 60 days’ written notice of termination or intent to move out as required by this paragraph and paragraph 36. If the number of days isn’t filled in, at least 30 days is required. In the event you fail to provide us with the required number of days' written notice of termination and intent to vacate coinciding with the lease expiration date, as required by this paragraph and paragraph 36, you acknowledge and agree that you will be liable to us for liquidated damages in the sum of $1400.00 (equal to one month’s rent) in accordance with Fla. Stat 83.575 (2). This liquidated damage amount is exclusive  to insufficient notice under this paragraph and paragraph 36, and does not limit collection rights with regard to other amounts potentially owed to us"

My question is can we legally charge the tenant? The statue mentions 15 days prior to the notice period which I believe would be 75 days but we sent out the notice 73 days. Our standard renewal offer didn't state what fees and penalties would be charged either. If we were to charge the tenant but then got the unit rented  before that month is up we would need to refund a prorated amount?