Suppose $m$ is a two-digit positive integer such that $6^{-1}\pmod m$ exists and $6^{-1}\equiv 6^2\pmod m$. What is $m$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose $m$ is a two-digit positive integer such that $6^{-1}\pmod m$ exists and $6^{-1}\equiv 6^2\pmod m$. What is $m$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
43
Suppose $m$ is a two-digit positive integer such that $6^{-1}\pmod m$ exists and $6^{-1}\equiv 6^2\pmod m$. What is $m$?
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