
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 $\{a_n\}$, where $a_2+a_3+a_4=15$ and $a_n > 0$, and $a_2$, $a_3+4$, $a_4+20$ are the first three terms of a geometric sequence $\{b_n\}$,  
(1) Find the general formulas for $\{a_n\}$ and $\{b_n\}$.  
(2) Let the sum of the first $n$ terms of the sequence $d_n= \frac {2}{a_na_{n+1}}$ be $T_n$, find $T_n$.  
(3) If the sequence $c_n=a_n\cdot b_n$, find the sum of the first $n$ terms of $\{c_n\}$, $S_n$.

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