
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 arithmetic sequence $\{a_{n}\}$ has a first term $a_{1}=1$, a common difference $d \neq 0$, and satisfies the condition $a_{3} \cdot a_{4} = a_{12}$.
(1) Find the general term formula for the sequence $\{a_{n}\}$;
(2) Let $b_{n} = a_{n} \cdot 2^{n}$, find the sum of the first $n$ terms, $T_{n}$, for the sequence $\{b_{n}\}$.

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