
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  $ {{a} _ {1}}, {{a} _ {2}}, \ldots, {{a} _ {n}} $  be permutation of numbers  $ 1,2, \ldots, n $ , where  $ n \geq 2 $ .
Find the maximum value of the sum   $$  S (n) = | {{a} _ {1}} - {{a} _ {2}} | + | {{a} _ {2}} - {{a} _ {3}} | + \cdots + | {{a} _ {n-1}} - {{a} _ {n}} |.  $$  

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