
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 $i = 1, 2, \cdots, n$, if $\left|x_{i}\right| < 1$ 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 minimum value of the positive integer $n$.

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