my current monitor is LG 23" IPS monitor

i'm happy with this monitor which served me for more than 20 months & i bought it as used unit @ reasonable price

recently 4k video is getting mature & the sources is easy to get , i intend upgrade to 4k resolution monitor

but my problem is my graphic card......does my radeon 7770 able to handle the 4k resolution ?

i'm using AMD phenom ii 560 + 4gb ddr3 ram

the only game i have is dota2 and csgo , i doesn't mind to run the game at 1080p on my 4k monitor if my gc unable to handle it but it can run right ?...due to the game doesn't need very high end card
my main purpose to buy that 4k monitor is just only because of 4k video , can my radeon 7770 able to play 4k video smooth ?
and what is the idle size for 4k monitor ?.....anything below 23inch is it under utilize ?
any brand or model can recommend ?

thank