
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 \(ABC\), the altitude \(BM\) is drawn, and a circle is constructed on it as a diameter, intersecting side \(AB\) at point \(K\) and side \(BC\) at point \(L\). Find the ratio of the area of triangle \(KLM\) to the area of triangle \(ABC\) if \(\angle A = \alpha\) and \(\angle C = \beta\).

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