
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
In the arithmetic sequence $\{a\_n\}$, the first term is $a\_1=1$. The sequence $\{b\_n\}$ satisfies $b\_n=(\frac{1}{2})^{a\_n}$, and $b\_1b\_2b\_3=\frac{1}{64}$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) Find the sum of the first $n$ terms, $S\_n$, for the sequence $\{a\_n b\_n\}$.

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