
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 $\{a_n\}$, $a_1=2$, and the common difference $d \neq 0$. $S_n$ represents the sum of the first $n$ terms, and it always holds that $S_{2n} = 4S_n$ for $n \in \mathbb{N}^+$.
(1) Find the general term formula for the sequence $\{a_n\}$;
(2) If $b_n = \frac{4}{\sqrt{a_n} + \sqrt{a_{n+1}}}$ for $n \in \mathbb{N}^+$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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