
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 integer triples  $(a,b,c)$  with  $a>0>b>c$  whose sum equal  $0$  such that the number  $$ N=2017-a^3b-b^3c-c^3a $$   is a perfect square of an integer.

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