
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
Given a positive integer \( n \) and a real number \( k > 0 \), what is the largest possible value for \( x_1 x_2 + x_2 x_3 + x_3 x_4 + \ldots + x_{n-1} x_n \), where \( x_i \) are non-negative real numbers with the sum equal to \( k \)?

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