What is the law regarding the reletting process?

Question Details: I will be reletting a college apartment and was told by managers that the rate the new tenant paid must be the same as my rate. However, their rates fluctuate very often with promos, deals, etc. and are currently much lower at this time than when I signed the lease earlier in the year. I was also told by leasing agents that upon paying the fee my unit would not be listed on their website or marketed at all as it seems and I would be solely responsible for finding a replacement tenant. Wouldn't it part of their duty to mitigate damages by offering a rate closer to the going current going rate of my unit granted how much their prices are altered? Also, would it be objectively reasonable for them to list my unit on their website? Some things to note Im in TX. They offer 1x1s, 2x2s, 3x3s and 4x4s some of which are upgraded with a more modern look and some are standard. I have a 4x4 upgraded unit and there are no more remaining mine would be the only one available after paying the fee. Also, I have not moved in yet as move-in day is on the 21st.

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