
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 real numbers \( x_{1}, x_{2}, \cdots, x_{1991} \) that satisfy the condition
\[
\sum_{i=1}^{1990} \left| x_{i} - x_{i+1} \right| = 1991,
\]
and \( y_{k} = \frac{1}{k} \sum_{i=1}^{k} x_{i} \) for \( k = 1, 2, \cdots, 1991 \), determine the maximum value of \( \sum_{i=1}^{1990} \left| y_{i} - y_{i+1} \right| \).

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