
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 \( i_{1}, i_{2}, \cdots, i_{10} \) be a permutation of \( 1, 2, \cdots, 10 \). Define \( S \) as \( S = \left|i_{1} - i_{2}\right| + \left|i_{3} - i_{4}\right| + \cdots + \left|i_{9} - i_{10}\right| \). Find all possible values of \( S \).

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