
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
Given that $\left|x_{i}\right| < 1$ for $i = 1, 2, \cdots, n$, and
$$
\left|x_{1}\right| + \left|x_{2}\right| + \cdots + \left|x_{n}\right| = 19 + \left|x_{1} + x_{2} + \cdots + x_{n}\right|,
$$

what is the minimum value of the integer $n$?

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