
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 $\{a_n\}$ where the common difference is nonzero, and it satisfies that $a_1 \neq 6$, $a_2$, $a_6$, $a_{14}$ form a geometric sequence.
(1) Determine the general term formula of the sequence $\{a_n\}$;
(2) Let $b_n = \frac{2}{(n+1)a_n}$, calculate 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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