
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 $\{a_n\}$ is an arithmetic sequence and $\{b_n\}$ is a geometric sequence, with $a_1=b_1=1$, $a_2 + b_3 = a_4$, and $a_3+ b_4 = a_7$:

(I) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$;  
(II) Let $c_n= \frac {1}{n}(a_{1}+a_{2}+\ldots+a_{n})(b_{1}+b_{2}+\ldots+b_{n})$, calculate the sum of the first $n$ terms $S_n$ of the sequence $\{c_n\}$.

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