You can check the cord by putting your multimeter in continuity mode using an audible sound to indicate continuity. Then connect to the neutral at each end (with the cord not connected to power) and bend the cord around. If you hear an interruption of the sound then you have a loose or broken wire. You could also borrow a cord from someone and see if it still triggers your broken neutral alarm. In your outlet you should be able to check the wiring terminations for tightness. I also have a Seek Thermal infrared camera adapter for my iPhone. I have used it to spot loose connections which typically get hot.
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