
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 decided to take Xiaohua on a driving tour to 10 cities during the holidays. After checking the map, Xiaohua was surprised to find that among any three of these cities, either all are connected by highways, or exactly two cities are not connected by a highway. How many highways exist among these 10 cities at least? (Note: There is at most one highway between any two cities.)

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