
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
Let  $N=30^{2015}$ .  Find the number of ordered 4-tuples of integers  $(A,B,C,D)\in\{1,2,\ldots,N\}^4$  (not necessarily distinct) such that for every integer  $n$ ,  $An^3+Bn^2+2Cn+D$  is divisible by  $N$ .

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