
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
Given a cross-country race with 5 players on each team, with points earned by the team based on the finishing position of each player (with the first place player earning 1 point, the second place player earning 2 points, and so on), determine the number of possible scores for the winning team.

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