
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

Given \( x_1, x_2, \cdots, x_{1993} \) that satisfy
\[
\begin{array}{l}
\left|x_1 - x_2\right| + \left|x_2 - x_3\right| + \cdots + \left|x_{1992} - x_{1993}\right| = 1993, \\
y_k = \frac{x_1 + x_2 + \cdots + x_k}{k}, \quad (k=1, 2, \cdots, 1993)
\end{array}
\]

What is the maximum possible value of \( \left|y_1 - y_2\right| + \left|y_2 - y_3\right| + \cdots + \left|y_{1992} - y_{1993}\right| \)?

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