
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
Let  $n\ge2$  be an integer and let  $x_1,x_2,\ldots,x_n$  be real numbers. Consider  $N=\binom n2$  sums  $x_i+x_j$ ,  $1\le i<j\le n$ , and denote them by  $y_1,y_2,\ldots,y_N$  (in an arbitrary order). For which  $n$  are the numbers  $x_1,x_2,\ldots,x_n$  uniquely determined by the numbers  $y_1,y_2,\ldots,y_N$ ?

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