
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 arithmetic sequence ${a_n}$ and geometric sequence ${b_n}$, $a_2=0$, $b_2=1$, and $a_3=b_3$, $a_4=b_4$.
(1) Find $a_n$ and $b_n$;
(2) Find the sum of the first $n$ terms $S_n$ of the sequence ${nb_n}$.

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