
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 $a_n = \frac{4n^2+k}{2n+1}$, and $\{a_n\}$ is an arithmetic sequence.  
(1) Find the value of $k$ and the sum of the first $n$ terms of $\{2^{a_n}\}$, denoted as $S_n$;  
(2) Let $b_n = \frac{na_na_{n+1}+2}{a_na_{n+1}}$, find the sum of the first $n$ terms of $\{b_n\}$, denoted as $T_n$.

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