
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 every positive integer  $n$  determine the least possible value of the expression
\[|x_{1}|+|x_{1}-x_{2}|+|x_{1}+x_{2}-x_{3}|+\dots +|x_{1}+x_{2}+\dots +x_{n-1}-x_{n}|\]
given that  $x_{1}, x_{2}, \dots , x_{n}$  are real numbers satisfying  $|x_{1}|+|x_{2}|+\dots+|x_{n}| = 1$ .

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