
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 a spherical planet, there are $2n$ fuel stations symmetrically positioned with respect to the center of the sphere (i.e., for each fuel station, there is another one located at its diametrically opposite point). Each fuel station has a certain amount of fuel stored, and the fuel is non-renewable. It is known that a car with an initially empty (but infinitely large capacity) fuel tank can start from any fuel station and, by selecting an appropriate route, refuel at each station it passes and reach the fuel station that is symmetric to the starting point. The car's fuel consumption rate per unit distance is constant.

Under these conditions, find the value of $n$ such that the car can traverse all the fuel stations on the planet by some route (the starting and ending points are not restricted).

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