In a seven-sided star (heptagram) shown, the vertices are labeled $A,B,C,D,E,F,$ and $G$. These letters are replaced by the numbers 1, 2, 3, 4, 5, 6, and 7, although not necessarily in that order. The sums of the numbers at the ends of the seven line segments forming the star polygon (e.g., $\overline{AB}$, $\overline{BC}$, etc., following the star's path) form an arithmetic sequence, although not necessarily in that order. What is the middle term of this arithmetic sequence?
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