I'm a long ways from being a farmer, but 24" sounds extreme. You almost have to have a multi year plan. plow it under (maybe 8-12 inches) First year plant something that is nitrogen fixing (depends on your zone, Peas maybe), maybe add some organic material, plow again. Then the next year plant Alfalfa or Rape Alfalfa mix. Both Rape and especially Alfalfa have deep roots, which will hopefully break up the hard pan.

It would take a serious tractor and an extreme chisel to get down 24". You might plow up a gas or electric line.

I usually swap labor with a Farmer and have him do my plowing for me. They know the soil and what it needs better than I do.

If you don't want hard pan, keep the tractor off it as much as possible.

Clay or sand doesn't have many nutrients in it, the good stuff is usually near the surface. Deep plowing may do more harm than good.