
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 $\{a_n\}$ with the first term $a_1=1$ and common difference $d\neq 0$, and a geometric sequence $\{b_n\}$ such that $a_1=b_1$, $a_2=b_2$, and $a_5=b_3$.  
(i) Find the general term formulas for sequences $\{a_n\}$ and $\{b_n\}$.  
(ii) Let sequence $\{c_n\}$ satisfy $\dfrac {c_1}{b_1} + \dfrac {c_2}{b_2} + \ldots + \dfrac {c_n}{b_n} = a_{n+1}$ for any $n\in\mathbb{N}^*$. Find the sum of the first $n$ terms $S_n$ of sequence $\{c_n\}$.

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