
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
The sum of  $n > 2$  nonzero real numbers (not necessarily distinct) equals zero. For each of the  $2^n - 1$  ways to choose one or more of these numbers, their sums are written in non-increasing order in a row. The first number in the row is  $S$ . Find the smallest possible value of the second number.

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