A laser is placed at the point \((3,5)\). The laser beam travels in a straight line. Larry wants the beam to hit and bounce off the \(y\)-axis, then hit and bounce off the \(x\)-axis, and finally hit the point \((7,5)\). Find the total distance the beam will travel along this path. The original answer is in the form \(k\sqrt{m}\), please give the value of \(k + m\).

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