
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
The country of HMMTLand has 8 cities. The government decides to construct several two-way roads between pairs of distinct cities. After construction, it turns out that each city can reach exactly 3 other cities via a single road, and for any pair of distinct cities, either exactly 0 or 2 other cities can be reached from both cities by a single road. Compute the number of ways HMMTLand could have constructed the roads.

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