
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

For which permutation \(a_1, a_2, \ldots, a_{2011}\) of the numbers \(1, 2, \ldots, 2011\) will the value of the expression

\[ \sum_{i=1}^{2010} \left| a_i - a_{i+1} \right| \]

be the greatest?

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