
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
$n$ ($n \geqslant 4$) soccer teams participate in a round-robin tournament. Each team plays every other team once. In each match, the winning team earns 3 points, the losing team earns 0 points, and in case of a draw, each team earns 1 point. After the tournament, the total points of each team form an arithmetic sequence with a common difference of 1. What is the maximum possible score for the team in last place?

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