
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 sequence $\{a\_n\}$ is a geometric sequence with the sum of the first $n$ terms denoted as $S\_n$, and $S\_n = λ \cdot 4^n - 3λ + 1 (λ \in \mathbb{R})$.

1. Find the general term formula for $\{a\_n\}$.
2. Let $b\_n = \log\_2 (S\_n + \frac{1}{2}) + 1$. Find the sum of the first $n$ terms, denoted as $T\_n$, for the sequence $\{ \frac{3b\_n}{4a\_n} \}$.

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