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There are numbers x-2, y+1, z+2 that form an arithmetic line, numbers x, y, z that form a geometric line, and numbers x-1, y-1, and

There are numbers x-2, y+1, z+2 that form an arithmetic line, numbers x, y, z that form a geometric line, and numbers x-1, y-1, and z+1 that form a geometric line. What is the sum of all possible values of y?

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