
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 sum of the first $n$ terms of a sequence is denoted by $S_n$. Given $a_n > 0$, and $a_n^2 + 2a_n = 4S_n - 1$.

(1) Find the general term formula for $\{a_n\}$.

(2) Let $b_n = \dfrac{1}{a_n a_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted by $T_n$.

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