Let's Meet in #1

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Let \(a\) and \(b\) \((a < b) \) be constants such that for any real number \(m\) satisfying \( a < m < b \), the two lines \[y=-2x+2, \;\; y=mx-2m+4\] intersect in the first quadrant. What is the largest possible value of \(b-a\)?

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