
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
Given the sequence {a<sub>n</sub>}, where a<sub>1</sub> = 3 and n(n+1)(a<sub>n</sub> - a<sub>n+1</sub>) = 2 for all n ∈ N*.

1. Find the general term formula for the sequence {a<sub>n</sub>}.
2. Let b<sub>n</sub> = $$\frac{a_{1} \cdot a_{2} \ldots a_{n}}{(n+1) \cdot 2^{n}}$$, find the sum of the first n terms, S<sub>n</sub>, of the sequence {b<sub>n</sub>}.

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