
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
Football teams $A, B, C, D,$ and $E$ play a round-robin tournament (each pair of teams plays one match), where the winning team earns 3 points, the losing team earns 0 points, and in case of a draw, both teams earn 1 point each. Given that the total points for teams $A, B, C,$ and $D$ are 1, 4, 7, and 8 respectively, determine the maximum and minimum points that team $E$ can earn.

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