
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 a Go club, there are 55 players with different rankings. The players decided to play a round-robin tournament where each player plays exactly one game against each other player. To make the tournament more interesting, some players were allowed to use a computer's assistance exactly once during the tournament. If a player using a computer's assistance plays against a player who is not, the one using the computer wins; otherwise, the player with the higher ranking wins. There are no ties in Go.

By the tournament's end, there are two players who each won more games than any of the two highest-ranked players. What could be the maximum number of players who did not use a computer's assistance?

Option 1: 45 players
Option 2: 55 players
Option 3: 35 players
Option 4: 50 players

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