
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 $\{a_{n}\}$, the sum $S_{n}$ of the first $n$ terms is related to the $n$th term $a_{n}$ by the equation $\frac{S_{n}}{a_{n}} = 1 + \frac{1}{r} + \frac{1}{r^2} + \cdots + \frac{1}{r^{n-1}}$, where $r$ is the common ratio of the geometric sequence.

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