Five rays $\overrightarrow{OA}$, $\overrightarrow{OB}$, $\overrightarrow{OC}$, $\overrightarrow{OD}$, and $\overrightarrow{OE}$ radiate in a clockwise order from $O$ forming four non-overlapping angles such that:
- $\angle EOD = 2\angle COB$,
- $\angle COB = 2\angle BOA$,
- $\angle DOC = 3\angle BOA$.

If $E$, $O$, $A$ are collinear with $O$ between $A$ and $E$, what is the degree measure of $\angle DOB$?

Let's think step by step and output the final answer within \boxed{}.
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