In base $10,$ $44 \times 55$ does not equal $3506.$ In what base does $44 \times 55 = 3506$?
<|im_start|>system
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<|im_start|>user
In base $10,$ $44 \times 55$ does not equal $3506.$ In what base does $44 \times 55 = 3506$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7
In base $10,$ $44 \times 55$ does not equal $3506.$ In what base does $44 \times 55 = 3506$?
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