If $x, y > 0$, $\log_y x + \log_x y = \frac{10}{3}$ and $xy = 144$, then find the value of $\frac{x+y}{2}$. The original answer is in the form of 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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