
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 a non-zero common difference arithmetic sequence $\{a_n\}$ satisfying $a_3 + a_8 = 20$, and $a_5$ is the geometric mean of $a_2$ and $a_{14}$,
(1) Find the general formula for the sequence $\{a_n\}$;
(2) Let sequence $\{b_n\}$ be defined by $b_n = \frac{1}{a_n a_{n+1}}$, then find the sum $S_n$ of the first $n$ terms of the sequence $\{b_n\}$.

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