
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 a right triangle $ABC$ with a right angle at $A$, a circle is constructed on the altitude $AD$ as its diameter. This circle intersects the side $AB$ at point $K$ and the side $AC$ at point $M$. The segments $AD$ and $KM$ intersect at point $L$. Find the acute angles of triangle $ABC$ given that $AK: AL = AL: AM$.

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