
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 lines connecting the vertices of the triangle with the center of the inscribed circle divide this circle into arcs whose lengths are in the ratio \( p: q: r \). Find the angles of triangle \( ABC \).

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