
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 $\{a_n\}$ that satisfies $a_3=7$, $a_5+a_7=26$, and $b_n= \frac{1}{a_n^2-1}\ (n\in\mathbb{N}^*)$, the sum of the first n terms of the sequence $\{b_n\}$ is denoted as $S_n$. Find the value of $S_{100}$.

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