An ice dam needs three things: snow on the roof, an attic warm enough to melt it from below, and a cold eave where the melt refreezes. Parma's lake-effect snow supplies the first; the other two are your attic's doing.
The fixes in order of impact: seal the attic floor's air leaks (hatches, can lights, plumbing stacks), bring insulation to an even depth, and keep soffit vents breathing so the roof deck stays cold. Ice-and-water shield under the eave shingles is the safety net for the storms that beat even a good attic.
What does not work: chopping at the dam (you will damage shingles), salt socks as a strategy, and heat cables as a first move. If a dam is leaking into a wall today, that is an emergency call; the attic work is the spring follow-up that ends the annual ritual.
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