
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 quadrilateral $ABCD$, $\angle BAD = 60^\circ$, $AB=AD$, and $AB=1$. Let $E$ be the midpoint of $BC$, and let $F$ be the point where the internal bisector of $\angle BCD$ intersects $BD$. Assume that the area of triangle $AEF$ is as large as possible. What is $\angle BCD$?
A) $60^\circ$
B) $72^\circ$
C) $80^\circ$
D) $90^\circ$
E) $100^\circ$

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