Please reason step by step, and put your final answer within \boxed{}.
Let \( A \), \( B \), and \( C \) be the remainders when the polynomial \( P(x) \) is divided by \( x-a \), \( x-b \), and \( x-c \), respectively.

Find the remainder when the same polynomial is divided by the product \( (x-a)(x-b)(x-c) \).
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