
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
In the sequences $\{a_n\}$ and $\{b_n\}$, $a_1=1$, $b_1=4$, the sum of the first $n$ terms of $\{a_n\}$, denoted as $S_n$, satisfies $nS_{n+1}-(n+3)S_n=0$, and $2a_{n+1}$ is the geometric mean of $b_n$ and $b_{n+1}$, where $n\in\mathbb{N}^+$.  
(1) Find the values of $a_2$ and $b_2$;  
(2) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$.

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