
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 20 students in the class. Each boy has made a list of all the girls in the class they find attractive (the list may be empty). It is known that there are no three boys whose lists contain the same number of girls. What is the minimum number of girls that could be in the class?

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