
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
From the ends of the arc \(AB\), which contains \(m^{\circ}\), chords \(AC\) and \(BD\) are drawn such that the angle \(DMC\) formed by their intersection is equal to the inscribed angle \(DNC\) in the arc \(CD\). Find the degree measure of this arc.

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