
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
given a positive integer  $n$ .
the set  $\{ 1,2,..,2n \}$  is partitioned into  $a_1<a_2<...<a_n $  and  $b_1>b_2>...>b_n$ .
find the value of :  $ \sum_{i=1}^{n}|a_i - b_i| $ 

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