
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 \(ABC\), the internal bisector \(CD\) is drawn. It is known that the center of the inscribed circle of triangle \(BCD\) coincides with the center of the circumscribed circle of triangle \(ABC\). Calculate the angles of triangle \(ABC\).

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