
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
For \( i=1,2, \cdots, n \), given \( \left|x_{i}\right|<1 \), and \( \left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|=2005+\left| x_{1} + x_{2}+\cdots+x_{n} \right| \). Find the smallest positive integer \( n \).

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