
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
Suppose there is an arithmetic sequence $\{a_n\}$ with common difference $d$ where $a_1=1$, and $a_1, a_2$, and $a_4$ form a geometric sequence. Let another sequence $b_n$ be defined as $b_n = \frac{1}{a_n^2 - 1}$. Find the sum of the first $n$ terms of the sequence $b_n$, denoted as $S_n$.

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