to move restlessly to and fro: to wander or flee as a homeless fugitive, and, by the shaking of the head over another's pain, to grieve with and console the suffering
The picture underneath every use of this word is the same: something moving repeatedly back and forth. A person driven from home wanders, and this is the verb behind Cain's sentence, "a fugitive and a wanderer." A reed in the water sways; under judgment the whole earth "reels to and fro like a drunkard."
From that same back-and-forth picture comes the shaking of the head. Turned toward an enemy it is mockery, the head wagged at someone's ruin. Turned toward a friend it is sympathy, and this is the word's most frequent use: to bemoan, to grieve with, to come and console. When the prophets ask "who will bemoan you?" over a fallen city, this is the verb they reach for.
Because one word runs all the way from fleeing to consoling, no single English word can follow it. It is close kin to נוּעַ, the twin verb of shaking and staggering that stands beside it in Cain's curse, and it overlaps the ordinary word for comforting, נָחַם, whenever it means to console the grieving.