
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 chess tournament using a round-robin format (each pair of players plays one game against each other), it is stipulated that: the winner of each game receives 1 point, the loser receives 0 points, and a draw results in each receiving 0.5 points. There are 8 players participating in this tournament, and it is known that their scores are all different. After ranking the players from highest to lowest score, the score of the player in second place is equal to the sum of the scores of the last four players. The following are five judgments:  
① The score of the player in second place must not exceed 6 points;  
② The score of the player in second place must not be less than 6 points;  
③ The score of the player in second place must be 6 points;  
④ The score of the player in second place could be 6.5 points;  
⑤ The score of the player in second place could be 5.5 points.  
The correct judgment numbers are (fill in the numbers of all correct judgments).

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