
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 $A, B, C, D, E$ are in a single round-robin tournament (each team plays one match against every other team). Each match results in a winner who gets 3 points and the loser gets 0 points, or a draw where both teams get 1 point each. Given that the total points for teams $A, B, C, D$ are 1, 4, 7, and 8 respectively, find the maximum and minimum points team $E$ can achieve.

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