
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 Three-Nine Kingdom, there are 100 cities, and each pair of cities is connected by at most one road. One day, the king ordered that each road should be designated as one-way, and also that each road should be painted either white or black. The Minister of Transportation proudly reported that after carrying out the order, it was possible to travel from any city to any other city by alternating the colors of the roads, starting with a white road. What is the minimum number of roads that could exist in this country? When traveling from one city to another, it is permissible to pass through intermediate cities any number of times.

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