Consider a positive integer \( n \) such that its representation in base \( 6 \) is \( AB_6 \) and its representation in base \( 4 \) is \( BA_4 \). If \( A \) and \( B \) are single-digit natural numbers in their respective bases, find the value of \( n \) in base \( 10 \). Let's think step by step and output the final answer within \boxed{}.
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