
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]


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Given that the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$, and $S\_n + \frac{1}{2}a\_n = 1 (n \in \mathbb{N}^*)$, and the sequence $\{b\_n\}$ is an arithmetic sequence with common difference $d \neq 0$, and it satisfies: $b\_1 = \frac{3}{2}a\_1$, $b\_2$, $b\_5$, $b\_{14}$ form a geometric sequence.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Let $c\_n = a\_n \cdot b\_n$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $T\_n$.

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