
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
BdMO National 2016 Higher Secondary 

<u>**Problem 4:**</u>
Consider the set of integers  $  \left \{ 1, 2, ......... , 100 \right \} $ . Let  $   \left \{ x_1, x_2, ......... , x_{100} \right \}$  be some arbitrary arrangement of the integers  $ \left \{ 1, 2, ......... , 100 \right \}$ , where all of the  $x_i$  are different. Find the smallest possible value of the sum, $S = \left | x_2 - x_1 \right | + \left | x_3 - x_2  \right | + ................+ \left |x_{100} - x_{99} \right | + \left |x_1 - x_{100} \right | $ .

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