
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 geometric sequence $\{a_{n}\}$ where $a_{3}=12$ and $a_{8}=\frac{3}{8}$, let $S_{n}$ denote the sum of its first $n$ terms.  
$(1)$ Find the general term formula $a_{n}$ of the sequence $\{a_{n}\}$.  
$(2)$ If $S_{n}=93$, find the value of $n$.

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