
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 regular hexagon $ABCDEF$ with its center at $J$, each of the vertices and the center is associated with one of the digits $1$ through $7$, with each digit used once, and the sums of the numbers on the lines $AJE$, $BJF$, $CJG$, and $DJH$ are all equal, determine the number of possible ways this can be done.

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