Let \( \triangle ABC \) be a triangle. Let point M be the point on BC that divided BC equally. Let D and E be points on AC that divided AC into three equal part.

F and G are points of intersection between AM and BD and BE, respectively.

If \( AF:FG:GM=a:b:c \) and a,b,c are co-prime number.

Find \( a+2b+3c \)

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