
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 that the sum of the first $n$ terms of the arithmetic sequence $\{a\}(_\{n\})$ is $S_n$, and the sum of the first $n$ terms of the geometric sequence $\{b\}(_\{n\})$ is $T_n$, with $a_1 = b_1 = 1$.

$S_3 = 6$, $T_3 = 7$

(1) Find the general term formulas for $\{a\}(_\{n\})$ and $\{b\}(_\{n\})$.

(2) Find the sum of the first $n$ terms of $\{a_n \cdot b_n\}$.

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