
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 $\{a\_n\}$, where $a\_1=2$, $a\_4=16$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) Suppose the arithmetic sequence $\{b\_n\}$ satisfies $b\_2=a\_2$, $b\_9=a\_5$, find the sum of the first $n$ terms, $S\_n$, for the sequence $\{b\_n\}$.

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