18. (12 points) As shown in Figure 1, in right trapezoid ABCD, $\mathrm { AD } / / \mathrm { BC } , ~ \angle \mathrm { BAD } = \frac { \pi } { 2 } , \mathrm { AB } = \mathrm { BC } = 1$, $\mathrm { AD } = 2$, E is the midpoint of AD, and O is the intersection of AC and BE. Fold $\triangle \mathrm { ABE }$ along BE to the position $\Delta \mathrm { A } _ { 1 } \mathrm { BE }$ as shown in Figure 2.

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  \includegraphics[alt={},max width=\textwidth]{2127fd6c-54be-499a-a5e1-4b2b0a02c393-2_186_355_2115_242}
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\caption{Figure 1}
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  \includegraphics[alt={},max width=\textwidth]{2127fd6c-54be-499a-a5e1-4b2b0a02c393-2_213_334_2074_651}
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\caption{Figure 2}
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(I) Prove that $\mathrm { CD } \perp$ plane $\mathrm { A } _ { 1 } \mathrm { OC }$;\\
(II) If plane $\mathrm { A } _ { 1 } \mathrm { BE } \perp$ plane BCDE, find the cosine of the dihedral angle between plane $\mathrm { A } _ { 1 } \mathrm { BC }$ and plane $\mathrm { A } _ { 1 } \mathrm { CD }$.