
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 non-empty set of numbers, the sum of its maximum and minimum elements is called the "characteristic value" of the set. $A\_1$, $A\_2$, $A\_3$, $A\_4$, $A\_5$ each contain $20$ elements, and $A\_1∪A\_2∪A\_3∪A\_4∪A\_5={x∈N^⁎|x≤slant 100}$, find the minimum value of the sum of the "characteristic values" of $A\_1$, $A\_2$, $A\_3$, $A\_4$, $A\_5$.

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