
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 isolated town of Sleepy Hollow, there are \(2n\) roundabouts each connecting exactly 3 roads. A series of bridges and tunnels ensure that roads only intersect at the roundabouts. Each road is two-way, and the roundabouts are oriented clockwise (it’s in England). Headless Horseman has just gotten his driver's license, and roundabouts make him very nervous. Therefore, at each roundabout, he takes the first exit he encounters. Upon leaving his house, he travels all the roads in the town, in both directions, before returning home. For which values of \(n\) is this possible?

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