
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 a certain town, there are $n \ (n \geqslant 3)$ villages. Some of these villages are connected by roads, and each road connects exactly two villages. There is at most one road between any two villages, and intersections of roads do not form crossroads but may have bridges or tunnels. It is known that any two villages can be reached through the roads, but if any arbitrary loop is closed for a bicycle race, the aforementioned connectivity no longer holds. Find the maximum number of roads.

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