
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 \(ABC\), a bisector \(BD\) is drawn. It is known that the center of the circumscribed circle around \(\triangle ABC\) coincides with the center of the inscribed circle in \(\triangle BCD\). Find the angles of \(\triangle ABC\).

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