Along the chain H > J ≥ K = L > M, which of the following is the strongest conclusion about H and M?

Compose the four links, all of which point the same way: H > J, J ≥ K, K = L, L > M. The equality passes straight through, and the run contains two strict links, so the composite is strict and H > M. That is the strongest of the four options. 'H ≥ M' and 'H ≠ M' are both true but each is weaker than H > M — 'H ≥ M' is the trap for a solver who lets the non-strict link J ≥ K dilute the whole chain, and 'H ≠ M' for one who concludes only that the two cannot coincide. 'Cannot be determined' is what a solver picks who treats K = L as a break in the chain, when in fact an equality preserves whatever relation reaches it.