
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 \( x_{1}, x_{2}, \cdots, x_{1993} \) satisfy:
\[
\left|x_{1}-x_{2}\right|+\left|x_{2}-x_{3}\right|+\cdots+\left|x_{1992}-x_{1993}\right|=1993,
\]
and
\[
y_{k}=\frac{x_{1}+x_{2}+\cdots+x_{k}}{k} \quad (k=1,2,\cdots,1993),
\]
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}
user