
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 a sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, and $2S\_n = 3^n \cdot p + m$, where $p$ and $m$ are constants. Also, $a\_1 = a\_2 = 3$.

1. Find the general formula for the sequence $\{a\_n\}$.
2. Let $b\_n = \log\_3 a\_n$, find the sum of the first $n$ terms, denoted as $T\_n$, for the sequence $\{a\_n \cdot b\_n\}$.

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