
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
Mother decides to take Xiaohua to 10 cities for a vacation by car. Xiaohua checked the map and was surprised to find that any three of these 10 cities have either all highways between them or only two of the cities have no highway between them. How many highways are there at least between these 10 cities? (Note: There can be at most one highway between any two cities.)

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