
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 that the common difference of the arithmetic sequence $\{a\_n\}$ is $d$, and the points $(a\_n, b\_n) (n \in \mathbb{N}^*)$ are on the graph of the function $f(x) = 2^x$.

(1) If $a\_1 = -2$, and the point $(a\_8, 4b\_7)$ is 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 $a\_1 = 1$, the tangent line to the graph of the function $f(x)$ at the point $(a\_2, b\_2)$ intersects the $x$-axis at $2 - \frac{1}{\ln 2}$. 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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