
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
A square and an isosceles triangle are inscribed in a circle and share a common vertex $D$. Designate the vertices of the square as $A$, $B$, $C$, and $D$ in clockwise order. The isosceles triangle has its unequal side along $DA$. The other vertex of the triangle is at point $E$, lying on the circle. If the angle $EDA$ is half the angle $EAD$, find the measure of the angle $DEA$.

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