
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 all terms are positive, $a\_2=4$, and $a\_4=16$.
(1) Find the common ratio $q$;
(2) If $a\_3$ and $a\_5$ are the 3rd and 5th terms of an arithmetic sequence $\{b\_n\}$, find the general term formula for the sequence $\{b\_n\}$.

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