17. (This question is worth 14 points) As shown in the figure, in the quadrangular pyramid $A - E F C B$, $\triangle A E F$ is an equilateral triangle, plane $A E F \perp$ plane $E F C B$, $E F / / B C$, $B C = 4$, $E F = 2 a$, $\angle E B C = \angle F C B = 60 ^ { \circ }$, and $O$ is the midpoint of $E F$. (I) Prove: $A O \perp B E$; (II) Find the cosine of the dihedral angle $F - A E - B$; (III) If $B E \perp$ plane $A O C$, find the value of $a$. [Figure]
17. (This question is worth 14 points)\\
As shown in the figure, in the quadrangular pyramid $A - E F C B$, $\triangle A E F$ is an equilateral triangle, plane $A E F \perp$ plane $E F C B$, $E F / / B C$, $B C = 4$, $E F = 2 a$, $\angle E B C = \angle F C B = 60 ^ { \circ }$, and $O$ is the midpoint of $E F$.\\
(I) Prove: $A O \perp B E$;\\
(II) Find the cosine of the dihedral angle $F - A E - B$;\\
(III) If $B E \perp$ plane $A O C$, find the value of $a$.\\
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