
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 the geometric sequence $\{a\_n\}$ and the arithmetic sequence $\{b\_n\}$, such that $a\_1 > 0$, $b\_1=a\_1-1$, $b\_2=a\_2$, $b\_3=a\_3$, and the sequence $\{a\_n\}$ is unique.
(1) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$;
(2) Find the sum of the first $n$ terms of the sequence $\{a\_n \cdot b\_n\}$.

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