
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 a football tournament, teams $A, B, C, D, E$ participated. Each team played exactly once with each other. In each match, 3 points were awarded for a win, 1 point for a draw, and 0 points for a loss.

It is known that by the end of the tournament:

- All teams scored different amounts of points.
- Team $A$ scored the most points, although it lost to team $B$.
- Teams $B$ and $C$ did not lose any match.
- Team $C$ scored fewer points than team $D$.

How many points did each team score?

Team $A$ scored:

Team $B$ scored:

Team $C$ scored:

Team $D$ scored:

Team $E$ scored:

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