19. (This question is worth 12 points). In the rectangular prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$, $A B = 16 , B C = 10 , A A _ { 1 } = 8$. Points $E$ and $F$ are on $A _ { 1 } B _ { 1 }$ and $D _ { 1 } C _ { 1 }$ respectively, with $A _ { 1 } E = D _ { 1 } F = 4$. A plane $\alpha$ passes through points $E$ and $F$ and intersects the faces of the rectangular prism, with the intersection lines forming a square. [Figure] (I) Draw this square in the figure (no need to explain the method or reasoning); (II) Find the ratio of the volumes of the two parts that plane $\alpha$ divides the rectangular prism into.
19. (This question is worth 12 points). In the rectangular prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$, $A B = 16 , B C = 10 , A A _ { 1 } = 8$. Points $E$ and $F$ are on $A _ { 1 } B _ { 1 }$ and $D _ { 1 } C _ { 1 }$ respectively, with $A _ { 1 } E = D _ { 1 } F = 4$. A plane $\alpha$ passes through points $E$ and $F$ and intersects the faces of the rectangular prism, with the intersection lines forming a square.\\
\includegraphics[max width=\textwidth, alt={}, center]{d02047a7-2e53-46f4-95bc-7a4508088779-4_350_542_900_340}\\
(I) Draw this square in the figure (no need to explain the method or reasoning);\\
(II) Find the ratio of the volumes of the two parts that plane $\alpha$ divides the rectangular prism into.\\