A frog is hopping from $(0,0)$ to $(8,8)$. The frog can hop from $(x,y)$ to either $(x+1,y)$ or $(x,y+1)$. The frog is only allowed to hop to point $(x,y)$ if $|y-x| \leq 1$. Compute the number of distinct valid paths the frog can take.

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