
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 an arithmetic sequence $\{a_n\}$ with a common difference $d \neq 0$ that satisfies $a_3 + a_7 = 20$, and $a_2$ is the geometric mean of $a_1$ and $a_4$.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) Let $b_n = 2^{a_n} + \frac{4}{a_na_{n+1}}$, 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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