
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  $100$  towns of a kingdom are connected by roads.It is known that for each two towns  $A$  and  $B$  connected by a road there is a town  $C$  which is not connected by a road with at least one of the towns  $A$  and  $B$ . Determine the maximum possible number of roads in the kingdom.

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