
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 natural numbers \( n \geq 2 \) does the inequality \( x_{1}^{2}+x_{2}^{2}+\ldots+x_{n}^{2} \geq p\left(x_{1} x_{2}+x_{2} x_{3}+\ldots+x_{n-1} x_{n}\right) \) hold for any real numbers \( x_{1}, x_{2}, \ldots, x_{n} \), if

a) \( p=1 \);

b) \( p= \frac{4}{3} \);

c) \( p= \frac{6}{5} \)?

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