Given positive real numbers $x$ and $y$ such that $\log_y x + \log_x y = 7$, what is $(\log_y x)^2 + (\log_x y)^2$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Given positive real numbers $x$ and $y$ such that $\log_y x + \log_x y = 7$, what is $(\log_y x)^2 + (\log_x y)^2$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
47
Given positive real numbers $x$ and $y$ such that $\log_y x + \log_x y = 7$, what is $(\log_y x)^2 + (\log_x y)^2$?
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