
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 of positive terms $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, it is known that $2S_n = \left(a_n + \frac{1}{2}\right)^2$ for all $n \in \mathbb{N}^*$.

(1) Find the general formula for the terms of the sequence $\{a_n\}$.
(2) Let $\{b_n\} = \frac{a_n + a_{n+1}}{a_n^2a_{n+1}^2}$. Find the sum of the first $n$ terms, denoted as $T_n$, for the sequence $\{b_n\}$.

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