
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
For each non-zero natural number $n$, there are points $A_n(x,0)$ and $B_n(y,0)$ on the x-axis, denoting the distance between these two points as $A_nB_n$, where the x-coordinates of $A_n$ and $B_n$ are the solutions to the system of equations
$$
\begin{cases}
\frac {1}{x}+ \frac {1}{y}=2n+1 \\
\frac {1}{x}- \frac {1}{y}=-1
\end{cases}
$$
Then the value of $A_1B_1+A_2B_2+\ldots+A_{2013}B_{2013}$ is ______________.

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