
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
There are 2015 pairwise distinct positive real numbers on the board. It turns out that for any number \( a > 0 \), the number of numbers on the board that are less than \( \frac{2014}{a} \) and the number of numbers greater than \( a \) have the same parity. What can the product of all the numbers be?

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