
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
The network of bus routes in the suburbs of Amsterdam is arranged such that:

a) each route has exactly three stops;

b) any two routes either have no common stops at all or have exactly one common stop. What is the maximum number of routes that can exist in this suburb if there are a total of 9 stops?

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