
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 the arithmetic sequence $\{a\_n\}$ that satisfies $(a\_1=f(x+1),a\_2=0,a\_3=f(x-1))$, where $f(x)=x^2-4x+2$.

(1) Find the general term formula for the sequence $\{a\_n\}$.

(2) When $d > 0$, let $\{b\_n=\frac{a\_n+4}{2^n}\}$. Find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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