
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
\(\left(x_{1}, x_{2}, \cdots, x_{2004}\right)\) is a permutation of \(1, 2, 3, \ldots, 2004\). Define \( M = \left|x_{1}-x_{2}\right| + \left|x_{3}-x_{4}\right| + \cdots + \left|x_{2003}-x_{2004}\right| \). What is the maximum value of \(M\)?

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