
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
There are 90 players in a league. Each of the 90 players plays exactly one match against each of the other 89 players. Each match ends with a win for one player and a loss for the other player, or with a tie for both players. Each player earns 1 point for a win, 0 points for a loss, and 0.5 points for a tie. After all matches have been played, the points earned by each player are added up. What is the greatest possible number of players whose total score can be at least 54 points?

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