
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
Three congruent circles are centered at points $A$, $B$, and $C$ such that each circle passes through the center of the other two circles. The line containing both $A$ and $B$ is extended to intersect the circles at points $D$ and $E$ respectively. The circles centered at $A$ and $C$ intersect at a point $F$ distinct from where they intersect with the circle centered at $B$. Calculate the degree measure of $\angle DFE$.

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