
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 function $f(x)=2\sin \pi x$ and the function $y= \frac {1}{1-x}$ have their graphs intersect at points in the interval $[-2,4]$ with the x-coordinates of these points being $x_{1}$, $x_{2}$, …, $x_{n}$. Calculate $\sum\limits_{i=1}^{n}x_{i}$.

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