
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 round-robin tournament format, a win earns 3 points, a draw earns 1 point, and a loss earns 0 points. There are six teams participating, and at the end of the tournament, the top three teams have the same score. Calculate the maximum possible score for these three teams.

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