
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 n rational numbers $x_{1}$, $x_{2}$, $\ldots$, $x_{n}$ satisfy $|x_{i}| \lt 1$ for $i=1,2,\ldots,n$, and $|x_{1}|+|x_{2}|+\ldots+|x_{n}|=19+|x_{1}+x_{2}+\ldots+x_{n}|$. Calculate the minimum value of $n$.

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