
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 diagram, point $E$ lies on line segment $AB$, and triangles $AED$ and $BEC$ are isosceles. Triangle $BCF$ with $\angle BCF = \angle BFC$ is also isosceles. Furthermore, $\angle DEC$ is still twice $\angle ADE$, and $\angle AED = 80^\circ$. What is the measure of $\angle EBF$ in degrees?

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