
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
In the country of Bethia, there are 125 cities, some of which are connected by express trains that do not stop at intermediate stations. It is known that any four cities can be circled in some order. What is the minimum number of city pairs connected by express trains?

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