
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
A tournament with 20 athletes was judged by 10 referees. Every athlete competed against every other athlete exactly once, and each match was judged by exactly one referee. After each game, both participants took a picture with the referee. A year after the tournament, a stack of all these photographs was found. It turned out that it wasn't possible to determine who was an athlete or a referee just by looking at the photographs. How many such undetermined people could there be?

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