
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 numbers \( x_{1}, \cdots, x_{1991} \) satisfy the condition
$$
\left|x_{1}-x_{2}\right|+\cdots+\left|x_{1990}-x_{1991}\right|=1991 ,
$$

where \( y_{k}=\frac{1}{k}\left(x_{1}+\cdots+x_{k}\right) \) for \( k = 1, \cdots, 1991 \). Find the maximum possible value of the following expression:
$$
\left|y_{1}-y_{2}\right|+\cdots+\left|y_{1990}-y_{1991}\right| .
$$

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