
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
Jia and Yi are playing a table tennis match, using a best of three sets system. In each set, the first player to reach 11 points and have the opponent score less than 10 points wins; if the score is tied at 10-10, the first player to gain a 2-point lead wins. The combined total score for Jia and Yi across the three sets is 30 points. When not considering the order of the scores, determine the total number of possible scores for the three sets.

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