
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 that the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $A\_n$, and $na_{n+1}=A_{n}+ \frac {3}{2}n(n+1)$, $a_{1}=2$; The sum of the first $n$ terms of the geometric sequence $\{b\_n\}$ is $B\_n$, and $B_{n+1}$, $B_{n}$, $B_{n+2}$ form an arithmetic sequence, $b_{1}=-2$.
(1) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$;
(2) Find the sum of the first $n$ terms, $S\_n$, of the sequence $\{a_{n} \cdot b_{n}\}$.

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