
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 right triangle $ABC$ with hypotenuse $AB$ is inscribed in a circle. Point $D$ is taken on the longer leg $BC$ such that $AC = BD$, and point $E$ is the midpoint of the arc $AB$ that contains point $C$. Find the angle $DEC$.

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