
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 \(ABC\), angle \(A\) is the largest angle. Points \(M\) and \(N\) are symmetric to vertex \(A\) with respect to the angle bisectors of angles \(B\) and \(C\) respectively. Find \(\angle A\) if \(\angle MAN = 50^\circ\).

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