
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
For which \( n \geq 2 \) is the inequality

$$
x_{1}^{2}+x_{2}^{2}+\ldots+x_{n}^{2} \geq x_{n}\left(x_{1}+x_{2}+\ldots+x_{n-1}\right)
$$

valid for all real values of the variables \( x_i \)?

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