
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
175 schoolchildren arrived at a health camp. Some of the children know each other, while others do not. It is known that any six schoolchildren can be settled in two three-bed rooms in such a way that all the schoolchildren in one room will know each other. What is the minimum number of pairs of schoolchildren who know each other that could have arrived at the camp?

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