
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
Let $f(x)$ be a non-zero function defined on $\mathbb{R}$ such that for any real numbers $x, y \in \mathbb{R}$, $f(x - y) = \frac{f(x)}{f(y)}$. Given that $f(1) = 2$ and $a_n = f(n)$ for $n \in \mathbb{N}^+$, find the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$.

A) $2^n - 1$
B) $2^n$
C) $2^{n+1} - 1$
D) $2^{n+1} - 2$

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