For how many ordered pairs $(A,B)$ where $A$ and $B$ are positive integers is $AAA_7+BBB_7=666_7?$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For how many ordered pairs $(A,B)$ where $A$ and $B$ are positive integers is $AAA_7+BBB_7=666_7?$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5
For how many ordered pairs $(A,B)$ where $A$ and $B$ are positive integers is $AAA_7+BBB_7=666_7?$
train