
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
The sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ is $S_n$, and $\{b_n\}$ is a geometric sequence satisfying $a_1=3$, $b_1=1$, $b_2+S_2=10$, and $a_5-2b_2=a_3$.  
(Ⅰ) Find the general formulas for sequences $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) Let $c_n= \frac {1}{2S_{n}}+b_n$, and let the sum of the first $n$ terms of sequence $\{c_n\}$ be $T_n$. Find $T_{2n}$.

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