Please reason step by step, and put your final answer within \boxed{}.
Given triangle \(ABC\) and line \(l\); \(A_1\), \(B_1\), and \(C_1\) are arbitrary points on line \(l\). Find the locus of the centroids of triangles with vertices at the midpoints of segments \(AA_1\), \(BB_1\), and \(CC_1\).
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