Consider a three-digit number \(\overline{ABC}\) where \(A\), \(B\), and \(C\) are its digits. The number \(\overline{ABC}\) is such that if the digits are rearranged to form the number \(\overline{BCA}\), the result is 198 more than \(\overline{ABC}\). Additionally, the sum of the digits \(A\), \(B\), and \(C\) is 15. Find the original number \(\overline{ABC}\). Let's think step by step and output the final answer within \boxed{}.
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