
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
For a given non-empty set of numbers, the sum of its largest and smallest elements is called the "characteristic value" of the set. Sets $A_1$, $A_2$, $A_3$, $A_4$, $A_5$ each contain 20 elements, and $A_1 \cup A_2 \cup A_3 \cup A_4 \cup A_5 = \{x \in \mathbb{N}^* | x \leq 100\}$. What is the minimum possible sum of the "characteristic values" of sets $A_1$, $A_2$, $A_3$, $A_4$, $A_5$?

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