
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 a sequence \( x_{1}, x_{2}, \ldots, x_{n} \) of real numbers, we define its price as
\[ \max_{1 \leqslant i \leqslant n}\left|x_{1} + \cdots + x_{i}\right|. \]

Given \( n \) real numbers, Dave and George want to arrange them into a sequence with a low price. Diligent Dave checks all possible ways and finds the minimum possible price \( D \). Greedy George, on the other hand, chooses \( x_{1} \) such that \( \left|x_{1}\right| \) is as small as possible; among the remaining numbers, he chooses \( x_{2} \) such that \( \left|x_{1} + x_{2}\right| \) is as small as possible, and so on. Thus, in the \( i^{\text{th}} \) step he chooses \( x_{i} \) among the remaining numbers to minimize the value of \( \left|x_{1} + x_{2} + \cdots + x_{i}\right| \). In each step, if several numbers provide the same value, George chooses one at random. Finally, he gets a sequence with price \( G \).

Find the least possible constant \( c \) such that for every positive integer \( n \), for every collection of \( n \) real numbers, and for every possible sequence that George might obtain, the resulting values satisfy the inequality \( G \leqslant c D \).

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