
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 gangsters, some of whom are hostile towards each other. Each gangster belongs to multiple gangs, and no two gangs have the same composition. It turns out that gangsters belonging to the same gang do not fight with each other, but if a gangster does not belong to a certain gang, he is hostile towards at least one of its members. What is the maximum number of gangs that could be in Chicago?

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