
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
The eight points  $A, B,. . ., G$  and  $H$  lie on five circles as shown. Each of these letters are represented by one of the eight numbers  $1, 2,. . ., 7$  and  $ 8$  replaced so that the following conditions are met:
(i) Each of the eight numbers is used exactly once.
(ii) The sum of the numbers on each of the five circles is the same.
How many ways are there to get the letters substituted through the numbers in this way?

(Walther Janous)
![Image](https://cdn.artofproblemsolving.com/attachments/5/e/511cdd2fc31e8067f400369c4fe9cf964ef54c.png)

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