
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
Find all triplets of integers  $(a,b,c)$  such that the number
   $$ N = \frac{(a-b)(b-c)(c-a)}{2} + 2 $$  is a power of  $2016$ .

(A power of  $2016$  is an integer of form  $2016^n$ ,where n is a non-negative integer.)

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