
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 given numbers \( n \geq 2 \) and \( a > 0 \), find the maximum value of the sum \( \sum_{i=1}^{n-1} x_i x_{i+1} \) subject to the conditions \( x_i \geq 0 \) for \( i = 1, \ldots, n \) and \( x_1 + \ldots + x_n = a \).

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