
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
Regular decagon $ABCDEFGHIJK$ has its center at $L$. Each of the vertices and the center are to be associated with one of the digits from $1$ through $12$, with each digit used exactly once, in such a way that the sums of the numbers on the lines $ALF$, $BLG$, $CLH$, $DLI$, $ELJ$ and $FKJ$ are all equal. Determine in how many ways this can be done.

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