
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 \( x_{1}, x_{2}, \cdots, x_{n} \) be \( n \) real numbers, each with an absolute value not less than 1. From the \( 2^{n} \) sums
\[
x_{A}=\sum_{j \in A} x_{s}, \quad A \subseteq X=\{1,2, \cdots, n\}
\]
at most \( C_{n}^{\left[\frac{n}{2}\right]} \) can be selected such that the difference between any two is less than 1.

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