
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
Given a circle with center at point \( O \) and radius 2. From the end of the segment \( OA \) intersecting the circle at point \( M \), a tangent \( AK \) is drawn to the circle such that \( \angle OAK = 60^\circ \). Find the radius of the circle that is tangent to the segments \( AK, AM \), and the arc \( MK \).

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