
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 $y=kx+k-1$ and the line $y=(k+1)x+k$ (where $k$ is a positive integer) and the x-axis form a triangle with area $S_k$. Find the value of $S_1+S_2+S_3+\cdots+S_{2011}$.

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