Mac Mini and 4K TV

Hello community!!

I've recently bought a 4K TV to use as monitor because I wanted a bigger resolution than the 1080p.

I have a Mac Mini (Late 2012) and I know it do not support 4K resolution but, as I saw in the Specs on "About my Mac", it says: "Support for up to two displays at 2560 by 1600 pixels, both at millions of colors". So, I know I cant have the 4K resolution but if I could have the 2560x1600 would be great already.

I have the 4K TV, I have a HDMI cable which supports 4K resolution plugged in my Mac Mini and on my 4K TV (both on HDMI ports without adapters), but still I see no option to set the resolution to 2560x1600 in my Monitor preferences. There is something I am doing wrong? Do I can have the 2560x1600 resolution on my 4K TV? How?

Hope someone can help me!

Thank you very much!