
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 an increasing function defined on the domain $\mathbb{R}$ such that for all $x, y \in \mathbb{R}$, $f(x+y)=f(x)+f(y)-1$. If the solution set of the inequality $f(x^{2}-x-3) < 3$ is ${x|-2 < x < 3}$, and $a_{n}=f(n)\;(n∈\mathbb{N}^{*})$, then the sum of the first $n$ terms of the sequence ${a_{n}}$ is $S_{n}=$ $\_\_\_\_\_\_\_\_$.

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