
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 with diameter \(BM\). This circle intersects side \(AB\) at point \(K\) and side \(BC\) at point \(Z\). Find the ratio of the area of triangle \(KZM\) to the area of triangle \(ABC\), given that \(\angle A = \alpha\) and \(\angle C = \beta\).

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