
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
Let \( x_{1}, \ldots, x_{n} \) be real numbers taking values of 0, +1, or -1. What is the minimum of
\[ \sum_{1 \leq i<j \leq n} x_{i} x_{j} ? \]

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