
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
Actually, the conclusion of the previous problem can be achieved with just 9 people. The problem is equivalent to having a complete graph with 9 vertices where each edge is colored either red or blue. One of the following will certainly exist: a red triangle or a completely blue quadrilateral. Similarly, one of the following will certainly exist: a completely red quadrilateral or a blue edge.

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