
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

...

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system
Given an arithmetic sequence {a<sub>n</sub>} with a common difference of d, and the solution set of the quadratic inequality a<sub>1</sub>x<sup>2</sup> - dx - 3 < 0 with respect to x is (-1, 3),
(I) Find the general term formula for the sequence {a<sub>n</sub>};
(II) If b<sub>n</sub> = $2^{( \frac {a_{n}+1}{2})}$ + a<sub>n</sub>, find the sum S<sub>n</sub> of the first n terms of the sequence {b<sub>n</sub>}.

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