
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 that the sequence $\{\frac{1}{a_n}\}$ is an arithmetic sequence and $a_3=\frac{1}{5}$, $a_2=3a_5$.
(1) Find the general term formula for $\{a_n\}$;
(2) If $b_n=a_n \cdot a_{n+1}$ (where $n\in \mathbb{N}^*$), find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted $S_n$.

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