
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 against each of the other teams. In each game, 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 earned different amounts of points;
- Team $A$ earned the most points, although it lost to team $B$;
- Teams $B$ and $C$ did not lose any game;
- Team $C$ earned fewer points than team $D$.

How many points did each team earn?

Team $A$ earned:

Team $B$ earned:

Team $C$ earned:

Team $D$ earned:

Team $E$ earned:

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