
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
Someone wants to invite 20 acquaintances - 9 ladies and 11 gentlemen - to their place. Each time, they invite 3 ladies and 2 gentlemen. How many invitations must be made so that every member of the group meets each other? How many times must each gentleman and lady attend the invitations?

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