
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
\( AB \) and \( AC \) are equal chords, and \( MAN \) is a tangent. The angular measure of arc \( BC \) that does not contain point \( A \) is \( 200^\circ \). Find the angles \( MAB \) and \( NAC \).

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