Given the equation of a line \( y = mx + b \) and that this line is perpendicular to the line passing through the points \((1, 2)\) and \((4, 5)\), find the value of \( m \) if the perpendicular bisector of the line segment joining these two points intersects the y-axis at \( y = 3 \). Let's think step by step and output the final answer within \boxed{}.
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