
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 function defined on $\mathbb{R}$ that is never zero, and for any $x, y \in \mathbb{R}$, it satisfies $f(x) \bullet f(y) = f(x + y)$. If ${a_1} = \frac{1}{2}, {a_n} = f(n), (n \in \mathbb{N}^+)$, determine the range of the sum of the first $n$ terms of the sequence ${{a_n}}$ denoted by ${S_n}$.

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