
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 sequences $\{a_{n}\}$ and $\{b_{n}\}$ are arithmetic and geometric, respectively, with $a_{1}=1$, $d > 0$, $a_{2}=b_{2}$, $a_{5}=b_{3}$, and $a_{14}=b_{4}$ for all $n\in\mathbb{N}^{*}$.
(I) Find the general terms for the sequences $\{a_{n}\}$ and $\{b_{n}\}$;
(II) Let $c_{n}=a_{n}\cdot b_{n}$. Find the sum of the first $n$ terms of the sequence $\{c_{n}\}$.

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