
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 tournament, there were 15 teams, each playing against every other team exactly once. A win earned a team 3 points, a draw 1 point, and a loss 0 points.

After the tournament ended, it was found that six teams had each scored at least \(N\) points. What is the maximum possible integer value of \(N\)?

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