
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 country, there are $n$ cities and $n$ nobles, with each noble owning one city. Nobles have constructed roads between some pairs of cities, and any given noble can construct at most one road between any two cities (note that there can be multiple roads between any two cities, but they belong to different nobles). Suppose the nobles have constructed $d$ roads in total. Some nobles now wish to form a "coalition" such that within the coalition, every city can be connected via roads that belong to members of the coalition (passing through cities outside the coalition is allowed, as long as the road belongs to a member of the coalition). However, the nobles discover that any coalition consisting of more than one and fewer than $n$ nobles cannot be formed. Determine the maximum possible value of $d$ under these conditions.

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