
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 the area of the right-angled triangle formed by the line $l_n: nx + (n+1)y - 1 = 0$ ($n \in \mathbb{N}^*$) and the coordinate axes be $S_n$. Find $$\lim_{n \to \infty}(S_{1}+S_{2}+S_{3}+\ldots+S_{n}).$$

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