
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
The sequence $\{a_n\}$ has a sum of the first $n$ terms denoted by $S_n$, where $S_n=2n^2+n$. The sequence $\{b_n\}$ satisfies $a_n=4\log_2{b_n}+3$, where $n\in\mathbb{N}^*$.

(1) Find $a_n$ and $b_n$.

(2) Find the sum of the first $n$ terms, $T_n$, of the sequence $\{a_n\cdot b_n\}$.

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