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Air/Train combo ticket from KLM

I am considering a ticket from the US through KLM which arrives in Amsterdam and then transfers me to Brussels via train. I assume I would get the train right at the airport in Amsterdam. Has anyone of you done this? Do you know if I would collect my luggage at the Amsterdam Airport off the plane and then take it with me on the train, or does the airlines take care of that? Also in reverse for return trip. The code for train is ZYR. Thanks!