
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 $x, y \in \mathbb{R}$, we have $f(x) \cdot f(y) = f(x+y)$. If $a_{1}= \frac {1}{2}$ and $a_{n}=f(n)$ for $n \in \mathbb{N}^{*}$, then the range of the sum of the first $n$ terms of the sequence $\{a_{n}\}$ is \_\_\_\_\_\_.

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