
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 a sequence $\{a_n\}$ with the sum of the first $n$ terms denoted by $S_n$, where $S_n = 2n^2 + n$ for $n \in \mathbb{N}$. There is another sequence $\{b_n\}$ satisfying $a_n = 4\log_2 b_n + 3$ for $n \in \mathbb{N}$.  
(1) Find $a_n$ and $b_n$;  
(2) Find the sum of the first $n$ terms of the sequence $\{a_n b_n\}$, denoted by $T_n$.

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