
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
What is the maximum number of factors of the form $\sin \frac{n \pi}{x}$ that can be crossed out on the left side of the equation

$\sin \frac{\pi}{x} \sin \frac{2 \pi}{x} \sin \frac{3 \pi}{x} \ldots \sin \frac{2015 \pi}{x}=0$

without changing the number of its natural roots?

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