
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
A round-robin table tennis tournament is held among three players: A, B, and C. The scoring system awards 2 points for a win, 0 points for a loss, and 1 point for a draw. How many different possible combinations of scores are there for the three players at the end of the tournament?

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