
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, there were 8 players. They scored respectively $7,6,4,4,3,2,1.5,$ and $0.5$ points. How many points did the players who took the top four places lose in their matches with the others?

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