
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 natural number $n$, if $n+6$ divides $n^3+1996$, then $n$ is called a lucky number of 1996. For example, since $4+6$ divides $4^3+1996$, 4 is a lucky number of 1996. Find the sum of all lucky numbers of 1996.

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