
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 \( n \), \( A n^3 + B n^2 + 2 C n + D \) is divisible by \( N \).

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