
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 triangle \(ABC\), it is known that \(\angle A = 60^\circ\) and \(\angle B = 45^\circ\). The extensions of the heights of triangle \(ABC\) intersect the circumcircle at points \(M\), \(N\), and \(P\). Find the ratio of the areas of triangles \(ABC\) and \(MNP\).

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