
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
Compute the value of the infinite series:
\[
\sum_{n=2}^{\infty} \frac{n^4 - 2n^3 + 3n^2 + 5n + 20}{3^n \cdot \left(n^4 + 4n^2 + 4\right)}
\]

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