
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
In Karabas Barabas theater, a chess tournament took place among actors. Each participant played every other participant exactly once. Winning a game awarded 1 solido, drawing a game awarded 0.5 solido, and losing a game awarded nothing. It turned out that among any three participants, there is one chess player who earned exactly 1.5 solidos in games against the other two. What is the maximum number of actors that could have participated in such a tournament?

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