
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
Let $\triangle ABC$ have angle $\angle ABC = 60^\circ$. Line segment $\overline{AF}$ bisects $\angle BAC$, $\overline{FD}$ bisects $\angle BCA$, and $\overline{DC}$ bisects $\angle BFA$. Determine the measure of angle $\angle ADC$.
- A) $100^\circ$
- B) $110^\circ$
- C) $120^\circ$
- D) $130^\circ$
- E) $140^\circ$

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