
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 $\left\{ a_n \right\}$ satisfies: $a_3=7$, $a_5+a_7=26$, the sum of the first $n$ terms of $\left\{ a_n \right\}$ is $S_n$.

$(1)$ Find $a_n$ and $S_n$;

$(2)$ Let $b_n=\frac{1}{a_n^2-1} \left( n\in \mathbb{N}^* \right)$, 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}
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