Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
Q:1/8=180
M:6/8
K:F
['cAG GDG', 'd2 A', 'f2 d']  
X:1
L:1/8
Q:1/8=180
M:6/8
K:F
|: d | cAG GDG | cAG G2 A | cAG GDG | cAF F2 d | cAG GDG | GDG GDG | FGA fed | cAF F2 :: (3A/B/c/ | 
 d2 A d2 A | cAG G2 A | d2 e fed | cAF F2 (3A/B/c/ | d2 A d2 A | cAF G2 A | FGA fed | cAF F2 :| e | 
 g2 e f2 d | cAG G2 e | g2 e f2 d | cAF F2 e | g2 e f2 d | gag f2 d | gfe fed | cAG G2 A | 
 BBB BdB | AAA AcA | GGG GFG | cAG G2 A | BBB BdB | AAA AcA | FGA fed | cAF F2 ||  