
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 quadrilateral $ABCD$, where $AB = BC = CD = DA$, and $AB$ is parallel to $CD$, point $E$ lies in the same half-plane relative to line $CD$ as point $A$ such that $\angle CDE = 120^{\circ}$. Point $F$ lies on $\overline{AD}$ such that $DE = DF$, and diagonals $AC$ and $BD$ intersect perpendicularly. Find the degree measure of $\angle AFE$.

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