
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 vertex \( B \), median \( BM \) is drawn. The incircle of triangle \( ABM \) touches sides \( AB \) and \( AM \) at points \( K \) and \( L \), respectively. It is known that lines \( KL \) and \( BM \) are parallel. Find the angle \( C \).

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