
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
The reals \( x_1, x_2, \ldots, x_n \) satisfy \( x_1^2 + x_2^2 + \ldots + x_n^2 + x_1 x_2 + x_2 x_3 + \ldots + x_{n-1} x_n = 1 \). What is the maximum possible value of \( |x_k| \)?

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