
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
On the water around a float moving counterclockwise along two circles are a water strider and a diving beetle. A rectangular coordinate system is introduced on the water surface, with the float (the common center of the circles) located at the point ( $0; 0$ ). The speed of the water strider is twice the speed of the beetle. At the initial moment of time, the water strider and the beetle are at points $M_{0}(2; 2 \sqrt{7})$ and $N_{0}(5; 5 \sqrt{7})$ respectively. Determine the coordinates of all positions of the beetle, at which the distance between the insects will be the greatest.

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