
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
Mom decides to take Xiaohua on a driving tour to 10 cities during the holidays. After checking the map, Xiaohua is surprised to find that among any three cities, either all three pairs of cities are connected by highways, or exactly one pair of cities is not connected by a highway. How many highways must have been constructed 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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