
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 an arithmetic sequence $\{a_n\}$, $a_1=3$, and the sum of the first $n$ terms is $S_n$. In a geometric sequence $\{b_n\}$, all terms are positive, $b_1=1$, and $b_2+S_2=12$, where the common ratio of the sequence $\{b_n\}$ is $q=\frac{S_2}{b_2}$.
(1) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$.
(2) Calculate the sum of the first $2n$ terms of the sequence $\{(-1)^na_nb_n\}$.

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