
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
Ten married couples, who were friends with each other, met for a meal together. First, they had an aperitif in the living room, and then all twenty people proceeded one by one to the dining room. What is the minimum number of people who must enter the dining room so that among them there will be:

1) at least one married couple;
2) at least two people of the same gender?

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