
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]


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Given that the second, third, and fourth terms of a geometric sequence $\{a_{n}\}$ are the second, fifth, and fourteenth terms of an arithmetic sequence $\{b_{n}\}$, and the first term of the arithmetic sequence $\{b_{n}\}$ is $b_{1}=1$, with a common difference $d \gt 0$.  
$(1)$ Find the general formulas for sequences $\{a_{n}\}$ and $\{b_{n}\}$;  
$(2)$ For any $n\in N^{*}$, let $\frac{c_{1}}{a_{1}}+\frac{c_{2}}{a_{2}}+\frac{c_{3}}{a_{3}}+\cdots+\frac{c_{n}}{a_{n}}=b_{n}$ hold. Find the value of $c_{1}+c_{2}+c_{3}+\cdots+c_{2023}$.

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