
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 cross country meet between 2 teams of 6 runners each, each runner's finish position contributes that number as a score to their team's total. The team with the lower score wins. Assuming there are no ties between the runners, determine the number of different winning scores that are possible, where the possible positions are 1 through 12 without repetitions.

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