
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
Let $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$, where all terms $a_n > 0$, and $S_n= \frac {1}{4}a_n^{2}+ \frac {1}{2}a_n- \frac {3}{4}$,  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$.  
(Ⅱ) Given $b_n=2^{n}$, find the value of $T_n=a_1b_1+a_2b_2+\ldots+a_nb_n$.

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