
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
Six soccer teams are playing a round-robin tournament where each team plays against each other exactly once. A draw awards each team 1 point, while a win awards the winning team 3 points and the losing team 0 points. After four rounds (each team has played against 4 teams), the total points for each team's four matches are all different. Given that the team with the third-highest total score has 7 points, and there have been 4 draws in total, determine the maximum and minimum points the team with the fifth-highest total score can have.

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