
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
A sequence is defined by \( A_{0}=0 \), \( A_{1}=1 \), \( A_{2}=2 \), and, for integers \( n \geq 3 \),
$$
A_{n}=\frac{A_{n-1}+A_{n-2}+A_{n-3}}{3}+\frac{1}{n^{4}-n^{2}}
$$

Compute \( \lim _{N \rightarrow \infty} A_{N} \).

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