
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 an acute, scalene triangle, four points have been marked: the incenter, the circumcenter, the centroid, and the orthocenter. Then, the triangle itself was erased. It turned out to be impossible to determine which center corresponds to each of the marked points. Find the angles of the triangle.

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