
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
Petya tells Vasya: "I constructed a scalene triangle \(ABC\) and drew the angle bisectors \(AM\) and \(CN\). It turned out that \(OM = ON\), where \(O\) is the point of intersection of the angle bisectors. Can you determine the measure of angle \(B\)?"

Vasya replies: "It is impossible for \(OM\) and \(ON\) to be equal in a scalene triangle."

Which of the boys is correct?

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