
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 the triangle \(ABC\), it is known that \(AB=BC\) and \(\angle BAC=45^\circ\). The line \(MN\) intersects side \(AC\) at point \(M\), and side \(BC\) at point \(N\). Given that \(AM=2 \cdot MC\) and \(\angle NMC=60^\circ\), find the ratio of the area of triangle \(MNC\) to the area of quadrilateral \(ABNM\).

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