
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 the regular octagon $ABCDEFGH$ with its center at $J$, and each of the vertices and the center associated with the digits 1 through 9, with each digit used once, such that the sums of the numbers on the lines $AJE$, $BJF$, $CJG$, and $DJH$ are equal, determine the number of ways in which this can be done.

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