
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
On the extension of side \(AC\) of the equilateral triangle \(ABC\) beyond point \(A\), a point \(M\) is taken, and circles are circumscribed around the triangles \(ABM\) and \(MBC\). Point \(A\) divides the arc \(MAB\) in the ratio \(MA:AB = n\). In what ratio does point \(C\) divide the arc \(MCB\)?

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