
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 round-robin table tennis tournament with 15 athletes, each athlete competes against every other athlete once. If athlete 1 wins $x_1$ matches, athlete 2 wins $x_2$ matches, ..., and athlete $n$ wins $x_n$ matches, find the value of $x_1 + x_2 + \ldots + x_n$.

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