
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 \(ABC\), let \(D\) be the intersection of \(BC\) with the bisector of \(\triangle BAC\). The center of the circumcircle of \(\triangle ABC\) coincides with the center of the inscribed circle of \(\triangle ADC\). Find the angles of \(\triangle ABC\).

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