
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
If a sequence of numbers \(a_{1}, a_{2}, \cdots\) satisfies, for any positive integer \(n\),
$$
a_{1}+a_{2}+\cdots+a_{n}=n^{3}+3 n^{2},
$$
then what is 
$$\frac{1}{a_{2}+2}+\frac{1}{a_{3}+2}+\cdots+\frac{1}{a_{2015}+2}?$$

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