
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 the following conditions: $a_{3}=7$, $a_{5}+a_{7}=26$, and the sum of the first $n$ terms of $\{a_{n}\}$ is denoted as $S_{n}$. <br/>$(1)$ Find $a_{n}$ and $S_{n}$; <br/>$(2)$ Let $b_{n}=\frac{1}{{{a}_{n}}^{2}-1}$ $(n\in N^{*})$, determine 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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