
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 sequence $\{a\_n\}$, its sum of the first $n$ terms is $S\_n=-\frac{1}{2}n^2+kn$, where $k\in\mathbb{N}_+$. The maximum value of $S\_n$ is 8.
(1) Determine the constant $k$ and find $a\_n$;
(2) Find the sum of the first $n$ terms, $T\_n$, of the sequence $\{\frac{9-2a\_n}{2^n}\}$.

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