
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
The sum of the x-coordinates and y-coordinates of all the intersection points of the graph of the function $y= \frac{1}{x}$ and the graph of the function $y=3\sin \pi x$ over the interval $-1\leqslant x\leqslant 1$ can be found by solving the equation $\frac{1}{x} = 3\sin \pi x$ for $x$ in the given interval.

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