
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 this diagram, $\triangle ABC$ is an equilateral triangle and within it is an inscribed triangle $\triangle DEF$, which is also equilateral. Label $\angle BFD$ as $a$, $\angle ADE$ as $b$, and $\angle FEC$ as $c$. Determine the values of these angles.
**A)** $a = b = c = 60^\circ$  
**B)** $a = 120^\circ, b = c = 60^\circ$  
**C)** $a = 60^\circ, b = c = 120^\circ$  
**D)** $a = b = c = 120^\circ$  
**E)** None of these

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