
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 9 cities in a country, some of which are connected by postal routes. For a letter to travel from one city to another, stamps equal to the number of routes required are needed (the route requiring the fewest number of routes is used). It is known that even if two cities are not directly connected by a route, it is always possible to send a letter from one to another.

During New Year's Eve, the mayors of all the cities sent each other congratulatory letters. What is the maximum number of stamps they could have all needed?

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