If $y = \sqrt{x^2 - 2x + 1} + \sqrt{x^2 + 2x + 1}$, find the expression for $y$ in terms of $x$. The original answer is in the form |ax + b| + |cx + d|. Please give the value of a + b + c + d.

Let's think step by step and output the final answer within \boxed{}.
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