
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
The sequence $\{a\_n\}$ satisfies the equation $S\_n = \frac{3}{2}a\_n - \frac{1}{2}a\_1$, where $S\_n$ is the sum of the first $n$ terms. Also, $a\_1 = 5$, $a\_3 + 5$, and $a\_4 - 15$ form an arithmetic sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If $b\_n = \frac{4 \log\_3 a\_n - 1}{a\_n}$, find the sum of the first $n$ terms, $T\_n$, for the sequence $\{b\_n\}$.

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