
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 $\{a\_n\}$ that satisfies $a\_2=0$ and $a\_6 + a\_8 = -10$.

1. Find the general term formula of the sequence $\{a\_n\}$.
2. Find the sum of the first $n$ terms of the sequence, denoted as $S\_n$.
3. Find the sum of the first $n$ terms of the sequence $\{ \frac{a\_n}{2^{n-1}} \}$, denoted as $T\_n$.

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