
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 triangle $ABC$, side $AC$ is twice the length of side $AB$. Let $D$ be on $\overline{AB}$ such that $AD$ is half of $AB$, and let $E$ be on $\overline{BC}$, such that $\angle BAE + \angle ACD = 180^\circ$. Let $F$ be the intersection of segments $AE$ and $CD$, and suppose that triangle $ADF$ is equilateral. What is $\angle ACB$?
A) $60^\circ$
B) $75^\circ$
C) $90^\circ$
D) $105^\circ$
E) $120^\circ$

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