
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 an arithmetic sequence $\{a_n\}$ with the first term $a$ and common difference $d$, and the equation $ax^2 - 3x + 2 = 0$ has solutions $1$ and $d$.

(1) Find the general formula for $\{a_n\}$ and the formula for the sum of the first $n$ terms.
(2) Find the sum of the first $n$ terms of the sequence $\{3^{n-1}a_n\}$, denoted as $T_n$.

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