
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
As shown in the diagram, plane $ABDE$ is perpendicular to plane $ABC$. Triangle $ABC$ is an isosceles right triangle with $AC=BC=4$. Quadrilateral $ABDE$ is a right trapezoid with $BD \parallel AE$, $BD \perp AB$, $BD=2$, and $AE=4$. Points $O$ and $M$ are the midpoints of $CE$ and $AB$ respectively. Find the sine of the angle between line $CD$ and plane $ODM$.

Present the answer in LaTex format: \boxed{Your answer}
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