
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 Magical Land, there are 100 cities, and some cities are connected by two-way air routes. Any two cities can be reached with no more than 11 transfers, and there is a unique way to do so. If it is not possible to reach city $A$ from city $B$ with 10 or fewer transfers, we call both cities peripheral. What is the largest number of peripheral cities that can exist in the land?

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