
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 $T_{n} = a_{1}b_{1} + a_{2}b_{2} + \ldots + a_{n}b_{n}$.

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