
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
Two people are playing a table tennis match, which is a best of three games. In each game, the first to score 11 points and have the opponent score less than 10 points wins, or if both players reach 10 points, the winner must score 2 points more than the opponent. The total scores of both players are 31 points. One person won the first game and eventually won the match. How many possible scores are there for the second game?

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