
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
There are 80 cities with two types of flight routes being operated: any city has direct flights to at least 7 other cities; any two cities can be connected through a finite number of direct flights. Find the smallest positive integer $k$ such that, no matter how the routes are arranged to meet the conditions, any city can reach any other city through at most $k$ direct flights.

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