
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
Calculate the sum of the infinite series defined by $\frac{1}{2! \cdot 3^1} + \frac{2}{3! \cdot 3^2} + \frac{3}{4! \cdot 3^3} + \dots$ where the $n$th term is $\frac{n}{(n+1)! \cdot 3^n}$.
A) $0.7388$
B) $0.8500$
C) $0.6000$
D) $0.9000$
E) $1.0000$

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