
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 the sequence \( x_{1}, x_{2}, \cdots, x_{1993} \) which satisfies \( \left| x_{1} - x_{2} \right| + \left| x_{2} - x_{3} \right| + \cdots + \left| x_{1992} - x_{1993} \right| = 1993 \), let \( y_{k} = \frac{x_{1} + x_{2} + \cdots + x_{k}}{k} \) for \( k=1, 2, \cdots, 1993 \). Find the maximum possible value of \( | y_{1} - y_{2} | + | y_{2} - y_{3} | + \cdots + | y_{1992} - y_{1993} | \).

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