
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 an arithmetic sequence $\{a\_n\}$ with a common difference $d \neq 0$, $a\_2=3$, and $a\_1$, $a\_3$, $a\_7$ form a geometric sequence.
(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) Let $b\_n = \begin{cases} 2^{a\_n}, & \text{if $n$ is odd} \\ \frac {2}{3}a\_n, & \text{if $n$ is even} \end{cases}$, and $S\_n$ denotes the sum of the first $n$ terms of the sequence $\{b\_n\}$. Find $S\_{16}$.

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