
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 a geometric diagram, quadrilateral $ABCD$ is inscribed with triangles $ABM$ and $CDN$ such that $AM = MB$, $DN = NC$, $\angle AMD = 58^\circ$, and $\angle DNC = 58^\circ$. What is the measure of $\angle MNC$?

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