
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
Given a convex quadrilateral \(ABCD\) with \(AB = BC = CA = CD\) and \(\angle ACD = 10^\circ\). Circumscribing triangle \(BCD\) is a circle \(\omega\) with center \(O\). Line \(DA\) intersects the circle \(\omega\) at points \(D\) and \(E\). Find the measure of angle \(EOA\) in degrees.

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