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Hi. I'm Smitty and I will be helping you with your problem.
What causes a water line to freeze up is a leaking water inlet valve. All of the water lines in refrigerators that are in the "freeze zone" are angled so that they drain to the dispenser to prevent just this from happening. If the valve has a small leak then there is constantly a little trickle of water going through it. this freezes, builds up , and clogs the line.
Replacing the water inlet valve will solve the problem.
Let me know if you require additional information.