
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 a sequence {a<sub>n</sub>}, where a<sub>1</sub> = 3 and the sum of the first n terms is S<sub>n</sub>.
(1) If {a<sub>n</sub>} is an arithmetic sequence and a<sub>4</sub> = 15, find S<sub>n</sub>.
(2) If {a<sub>n</sub>} is a geometric sequence and $$\overset{lim}{n\rightarrow \infty }S_{n}＜12$$, find the range of the common ratio q.

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