
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 $a_{2}=4$ and $2a_{4}-a_{5}=7$, and a geometric sequence $\{b_{n}\}$ with a common ratio not equal to $-1$ where $b_{3}=4$ and $b_{4}+b_{5}=8(b_{1}+b_{2})$.<br/>$(1)$ Find the general formulas for $\{a_{n}\}$ and $\{b_{n}\}$;<br/>$(2)$ Let ${c}_{n}=\frac{3}{{a}_{n}•{a}_{n+1}}(n∈{N}^{*})$, find the sum of the first $n$ terms of $\{c_{n}\}$ denoted as $S_{n}$.

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