
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
Given that there are seven teams that play each other once in a tournament, with a win earning $3$ points, $0$ points for any draw where both teams earn $0$ points, and $1$ point for each team in a non-zero draw, and the top four teams earned the same number of total points, calculate the greatest possible number of total points for each of the top four teams aside any draw that results in $0$ points for both teams.

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