
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 schools, A and B, each send out 5 students to participate in a long-distance race. The rules are: The $K$th student to reach the finish line scores $K$ points (no students tie for any position). The school with the lower total score wins. How many possible total scores can the winning team have?

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