
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
An island has  $10$  cities, where some of the possible pairs of cities are connected by roads. A *tour route* is a route starting from a city, passing exactly eight out of the other nine cities exactly once each, and returning to the starting city. (In other words, it is a loop that passes only nine cities instead of all ten cities.) For each city, there exists a tour route that doesn't pass the given city. Find the minimum number of roads on the island.

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