
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 non-negative numbers \( x_{1}, x_{2}, \ldots, x_{n} \) have a sum of 1.

How large can the value of 
\[ x_{1} x_{2} + x_{2} x_{3} + \ldots + x_{n-2} x_{n-1} + x_{n-1} x_{n} \] 
be?

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