
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  $m$  be a positive integer. Determine the smallest positive integer  $n$  for which there exist real numbers  $x_1, x_2,...,x_n \in (-1, 1)$  such that  $|x_1| + |x_2| +...+ |x_n| = m + |x_1 + x_2 + ... + x_n|$ .

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