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What I have seen over the years from the repair guys is they remove the back panel on the rear of the fridge for full drain tube access and clean it from there. It is model-specific, so remove the back rear panel first and see if you can access there first as that is the easiest to get to. What you are describing is a clogged drain. When the water can’t drain, it puddles and freezes. Time for a good cleaning, and you will be set for many years to come. Defrost it, clean it thoroughly, replace the tube, and you will see no more ice build-up.