
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 $A, B, C, D, E$ each played against every other team exactly once. The scoring system awarded 3 points for a win, 1 point for a draw, and 0 points for a loss.

At the end of the tournament, the following conditions are known:

- All teams scored a different number of points.
- Team $A$ scored the most points, despite losing to team $B$.
- Teams $B$ and $C$ did not lose any games.
- 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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