
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
The triangle \(ABC\) is isosceles at \(C\), and let \(\Gamma\) be its circumcircle. Let \(M\) be the midpoint of the arc \(BC\) of \(\Gamma\) that does not contain \(A\), and let \(N\) be the point where the parallel to \(AB\) through \(M\) intersects \(\Gamma\) again. It is known that \(AN\) is parallel to \(BC\). What are the measures of the angles of \(ABC\)?

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