
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 prefix sum of the sequence $\{a\_n\}$ is $S\_n$, and $S\_n = 2 - \frac{1}{2^{n-1}}$, and $\{b\_n\}$ is an arithmetic sequence with $a\_1 = b\_1$ and $a\_2(b\_2 - b\_1) = a\_1$.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Let $c\_n = \frac{b\_n}{a\_n}$. Find the prefix sum $T\_n$ of the sequence $\{c\_n\}$.

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