
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
A geometric sequence with a ratio \( r \neq 0 \) is a sequence of numbers \( s_{0}, s_{1}, s_{2}, \ldots \) which satisfies for every index \( k \): \( s_{k+1} = s_{k} \times r \). Determine an expression for \( s_{n} \) as a function of \( s_{0}, r \), and \( n \).

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