
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 $\left\{a_{n}\right\}$, where $a_{1}=3$ and the sum of the first $n$ terms is $S_{n}$.

(1) If $\left\{a_{n}\right\}$ is an arithmetic sequence and $a_{4}=15$, find $S_{n}$.

(2) If $\left\{a_{n}\right\}$ is a geometric sequence and $\lim\limits_{n\rightarrow \infty }S_{n} \lt 12$, find the range of values for the common ratio $q$.

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