
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 $\{a_{n}\}$ is an arithmetic sequence with a non-zero common difference, $a_{2}=3$, and $\log _{2}a_{1}$, $\log _{2}a_{3}$, $\log _{2}a_{7}$ form an arithmetic sequence. Find:<br/>
$(1)$ The general formula for the sequence $\{a_{n}\}$;<br/>
$(2)$ If the sequence $\{b_{n}\}$ satisfies ${b_n}=\frac{1}{{{a_n}{a_{n+1}}}$, find the sum of the first $n$ terms $S_{n}$ of the sequence $\{b_{n}\}$.

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