
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 the men's Olympic football group stage, each group consists of four teams, and each team plays against each other once. A win earns a team 3 points, a loss earns 0 points, and a draw earns each team 1 point. After all group stage matches are completed, the two teams with the highest points in each group advance to the next round (if teams are tied on points, there are additional tiebreaker rules). In all possible scenarios where a team can advance, what is the minimum number of points a team can have to advance? Please provide the reasoning.

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