
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
Consider an arithmetic sequence $\{a\_n\}$ with a common difference of $d$. The points $(a\_n, b\_n)$ lie on the graph of the function $f(x) = 2^x$ ($n \in \mathbb{N}^*$).

(1) If $a\_1 = -2$, and the point $(a\_8, 4b\_7)$ lies on the graph of the function $f(x)$, find the sum of the first $n$ terms of the sequence $\{a\_n\}$, denoted as $S\_n$.

(2) If $a\_1 = 1$, $a\_2 = 2$, find the sum of the first $n$ terms of the sequence $\{\frac{a\_n}{b\_n}\}$, denoted as $T\_n$.

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