
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 football league, there are eight teams that play each other twice in a season. Each team receives 3 points for a win, 1 point for a draw, and 0 points for a loss. Additionally, if a team wins without conceding a goal, they receive an extra 1 point as a bonus. Given that the top four teams all have the same number of total points, calculate the maximum number of points that each of these top four teams can earn.

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