
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 the arithmetic sequence \(\left\{a_{n}\right\}\) satisfying: \(a_{3}=7, a_{5}+a_{7}=26\), and the sum of the first \(n\) terms of \(\left\{a_{n}\right\}\) is \(S_{n}\).

(1) Find \(a_{n}\) and \(S_{n}\).

(2) Let \(b_{n}=\frac{1}{a_{n}^{2}-1} \left( n \in \mathbf{N}_{+} \right)\). Find the sum of the first \(n\) terms of the sequence \(\left\{b_{n}\right\}\), denoted as \(T_{n}\).

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