
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
Points \( P \) and \( Q \) are the midpoints of the arcs \( KL \) and \( LM \) of the circumcircle of triangle \( KLM \). \( LS \) is the angle bisector of this triangle. It is given that \(\angle KLM = 2 \angle KML\) and \(\angle PSQ = 90^\circ\). Find the angles of triangle \( KLM \).

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