
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 radius \( OM \) of the circle with center at point \( O \) and the chord \( KQ \) intersect at point \( A \). The lengths of segments \( OM \) and \( OA \) are \( r \) and \( a \) respectively, with \( \angle KAM = \alpha < 90^\circ \).

Find the radius of the circle that touches the segments \( AK \), \( AM \), and the arc \( MK \).

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