
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 angle bisectors \(AK\) and \(CL\) and the median \(BM\) are drawn. It turns out that \(ML\) is the angle bisector of \(\angle AMB\) and \(MK\) is the angle bisector of \(\angle CMB\). Find the angles of triangle \(ABC\).

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