
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 $\{a_{n}\}$ with a common difference $d > 0$, and $a_{1}⋅a_{6}=11$, $a_{3}+a_{4}=12$.
1. Find the general term formula of the sequence $\{a_{n}\}$.
2. Find the sum of the first $n$ terms, denoted as $T_{n}$, of the sequence $\{\frac{a_{n+1}-2a_{n}}{2^{n+1}}\}$.

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