
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
Given a line $nx + (n+1)y = \sqrt{2}$ $(n \in \mathbb{N}^{*})$ forms a triangle with the coordinate axes, and the area of this triangle is denoted as $S_n$. Calculate the value of $S_1 + S_2 + S_3 + \ldots + S_{2013}$.

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