
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
Determine all the integers \( n > 1 \) such that
$$
\sum_{i=1}^{n} x_{i}^{2} \geq x_{n} \sum_{i=1}^{n-1} x_{i}
$$
for all real numbers \( x_{1}, x_{2}, \ldots, x_{n} \).

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