
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 \( x_{1}, x_{2}, \ldots, x_{n} \) be real numbers with absolute values less than 1. What is the minimum value of \( n \) such that

\[ 
\left| x_{1} \right| + \left| x_{2} \right| + \ldots + \left| x_{n} \right| = 1989 + \left| x_{1} + x_{2} + \ldots + x_{n} \right| 
\]

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