What is the average of all positive integers that have three digits when written in base $5$, but two digits when written in base $8$? Write your answer in base $10$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the average of all positive integers that have three digits when written in base $5$, but two digits when written in base $8$? Write your answer in base $10$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
44
What is the average of all positive integers that have three digits when written in base $5$, but two digits when written in base $8$? Write your answer in base $10$.
train