
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 an isosceles triangle \(ABC\) with an obtuse angle \(A\) equal to \(\alpha\), altitudes \(BN\) and \(CM\) are drawn.

Find the ratio of the area of quadrilateral \(BMNC\) to the area of triangle \(ABC\).

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