
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
In the Land of Fools, there are \(N^2\) cities arranged in a square grid, with the distance between neighboring cities being 10 km. The cities are connected by a road system consisting of straight sections that are parallel to the sides of the square. What is the minimum length of such a road system if it is known that it is possible to travel from any city to any other city?

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