
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 sequence $\{a\_n\}$ is an arithmetic sequence satisfying $a\_1=2$ and $a\_4=8$, and the sequence $\{b\_n\}$ is a geometric sequence satisfying $b\_2=4$ and $b\_5=32$.
(I) Find the general term formula for both sequences $\{a\_n\}$ and $\{b\_n\}$.
(II) Find the sum $S_n$ of the sequence $\{a_n+b_n\}$ for the first $n$ terms.

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