
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 first three terms of the arithmetic sequence $\{a_n\}$ are $1$, $a$, $b$, and the first three terms of the geometric sequence $\{b_n\}$ with a common ratio not equal to $1$ are $4$, $2a+2$, $3b+1$.

(I) Find the general term formulas for the sequences $\{a_n\}$ and $\{b_n\}$.
(II) Let $$c_{n}= \frac {2}{a_{n}(log_{ \sqrt {2}}b_{n}-1)}$$, find the sum of the first $n$ terms, $S_n$, of the sequence $\{c_n\}$.

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