
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 two congruent equilateral triangles $ABC$ and $BDE$ such that the angle $ABD$ is greater than $120^\circ$ and less than $180^\circ$, and the points $C$ and $E$ are on the same side of the line $AD$. The intersection of $CD$ and $AE$ is denoted by $F$.

Determine the measure of the angle $AFD$.

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