
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 $\{a\_n\}$ with a non-zero common difference, $a\_1=3$, $a\_5=7$.
(I) Find the general term $a\_n$ of the sequence;
(II) If the sequence $\{b\_n\}$ is defined as $b\_n=2^{a\_n-2}$, find the sum $S\_n$ of the first $n$ terms of the sequence.

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