
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 Chicago, there are 36 criminal gangs, some of which are in conflict with each other. Each gangster belongs to multiple gangs, and any two gangsters belong to different sets of gangs. It is known that no gangster belongs to two gangs that are in conflict with each other. Furthermore, it turns out that each gang, which does not include a certain gangster, is in conflict with some gang that includes that gangster. What is the maximum number of gangsters that can be in Chicago?

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