
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 the acute-angled triangle \(ABC\), the segments \(BO\) and \(CO\), where \(O\) is the circumcenter, are extended to intersect the sides \(AC\) and \(AB\) at points \(D\) and \(E\) respectively. It is given that \(\angle BDE = 50^\circ\) and \(\angle CED = 30^\circ\). Find the angles of triangle \(ABC\).

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