
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
Let $\{a_n\}$ be an arithmetic sequence with a non-zero common difference. Given $a_1 = 3$, and that $a_1$, $a_4$, and $a_{13}$ form a geometric sequence.

(I) Find the general formula for the sequence $\{a_n\}$;

(II) Let $b_n = 2^n a_n$, find the sum of the first n terms of the sequence $\{b_n\}$.

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