
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 the integer \( n > 1 \) and the real number \( a > 0 \), determine the maximum of \(\sum_{i=1}^{n-1} x_{i} x_{i+1}\) taken over all nonnegative numbers \( x_{i} \) with sum \( a \).

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