
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
A sequence $\{a\_n\}$ has a sum of its first $n$ terms denoted as $S\_n$. For any positive integer $n$, $a\_n > 0$ and $4S\_n = (a\_n + 1)^2$.

1. Find the general formula for the $n$th term of the sequence $\{a\_n\}$.
2. Let $b\_n = \frac{a\_n}{3^n}$ and $T\_n = b\_1 + b\_2 + \dots + b\_n$. Find $T\_n$.

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