
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
Some of the towns in a country are connected with bidirectional paths, where each town can be reached by any other by going through these paths. From each town there are at least  $n \geq 3$  paths. In the country there is no such route that includes all towns exactly once. Find the least possible number of towns in this country (Answer depends from  $n$ ).

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