
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
In the given configuration, $CD$ is the diameter of a semicircle with center $O$. Point $A$ is on the extension of $DC$ beyond $C$, and point $E$ is on the semicircle. $B$ is the intersection of line segment $AE$ with the semicircle (distinct from $E$). If $AB = OE$, and $\angle EOD = 30^\circ$, find the measure of $\angle BAO$.

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