
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
There is a saucer of milk on the floor, around which a kitten and a puppy are walking along two circles. The speed of the kitten is half the speed of the puppy. A rectangular coordinate system is introduced on the plane of the floor, with the saucer (the common center of the circles) located at the point $O(0 ; 0)$. The kitten moves clockwise, and the puppy moves counterclockwise. Initially, the kitten and the puppy are at the points $M_{0}(-6 ; 0)$ and $N_{0}(2 ; 2 \sqrt{3})$, respectively. Determine the coordinates of all positions of the kitten where the distance between the animals will be the shortest.

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