
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
The circle constructed on the altitude \( AD \) of the right triangle \( ABC \) as a diameter intersects the leg \( AB \) at point \( K \) and the leg \( AC \) at point \( M \). The segment \( KM \) intersects the altitude \( AD \) at point \( L \). It is known that the segments \( AK \), \( AL \), and \( AM \) form a geometric progression (i.e., \(\frac{AK}{AL} = \frac{AL}{AM}\)). Find the acute angles of triangle \( ABC \).

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