
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
Each of \( x_1, x_2, \ldots, x_n \) is -1, 0, or 1. What is the minimal possible value of the sum of all \( x_i x_j \) with \( 1 \leq i < j \leq n \)?

Is the answer the same if the \( x_i \) are real numbers satisfying \( 0 \leq |x_i| \leq 1 \) for \( 1 \leq i \leq n \)?

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