
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 math competition, the possible scores for each problem for each participating team are 0 points, 3 points, or 5 points. By the end of the competition, the sum of the total scores of three teams is 32 points. If the total score of any single team can reach 32 points, how many different possible combinations are there for the total scores of these three teams?

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