
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 the arithmetic sequence $\{a_n\}$ satisfying:
$$
a_3 = 7, a_5 + a_7 = 26,
$$
where $S_n$ is the sum of the first $n$ terms of $\{a_n\}$.
(1) Find $a_n$ and $S_n$;
(2) Let $b_n = \frac{1}{a_n^2 - 1}$ for $n \in \mathbf{Z}_{+}$. Find the sum of the first $n$ terms of the sequence $\{b_n\}$.

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