
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 a common difference $d>0$, and $a_2$, $a_5$, $a_{14}$ happen to be the first three terms of a geometric sequence $\{b_n\}$.  
(I) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$.  
(II) If for sequence $\{c_n\}$ and any natural number $n$, $$\frac{1}{c_n} = (a_n + 3) \cdot \log_{3}b_n$$, find the sum of the first $n$ terms of sequence $\{c_n\}$.

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