
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 a non-zero common difference arithmetic sequence $\{a_n\}$ has a sum of its first 4 terms equal to 10, and $a_2$, $a_3$, and $a_7$ form a geometric sequence,
(I) Find the general term $a_n$ formula.
(II) Let $b_n = 2^{a_n}$, determine the sum of the first $n$ terms of the sequence $\{b_n\}$, $S_n$.

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