
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 $\{a_n\}$ satisfies: $a_2=5$, $a_4+a_6=22$, and the sum of the first $n$ terms of $\{a_n\}$ is $S_n$  
$(1)$ Find $a_n$ and $S_n$;  
$(2)$ Let $b_n= \frac {1}{a_n^2-1}$ $(n\in\mathbb{N}^*)$, find 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}
user