
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 line $kx + (k+1)y = 1$ ($k \geq 1$ and $k$ is a positive integer) form a triangle with the two coordinate axes, and let the area of this triangle be $S_k$ ($k=1,2,\ldots,2011$). Calculate the sum $S_1 + S_2 + \ldots + S_{2011}$.

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