
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
Let the real numbers \( x_{1}, x_{2}, \cdots, x_{2008} \) satisfy the condition \( \left|x_{1} - x_{2}\right| + \left|x_{2} - x_{3}\right| + \cdots + \left|x_{2007} - x_{2008}\right| = 2008 \). Define \( y_{k} = \frac{1}{k} (x_{1} + x_{2} + \cdots + x_{k}) \) for \( k = 1, 2, \cdots, 2008 \). Find the maximum value of \( T = \left|y_{1} - y_{2}\right| + \left|y_{2} - y_{3}\right| + \cdots + \left|y_{2007} - y_{2008}\right| \).

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