
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
Around a flower on the same plane, a bumblebee and a bee fly along two circles. The speed of the bee is one and a half times the speed of the bumblebee. A rectangular coordinate system is introduced on the plane, with the flower (center of the circles) located at the point $O(0 ; 0)$. The bee moves clockwise, and the bumblebee moves counterclockwise. At the initial moment of time, the bee and the bumblebee are at points $M_{0}\left(-\frac{1}{2} ; \frac{\sqrt{3}}{2}\right)$ and $N_{0}(2 ; 0)$ respectively. Determine the coordinates of all positions of the bumblebee where the distance between it and the bee is the shortest.

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