
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
Petya wrote down 10 integers on the board (not necessarily distinct). He then calculated the pairwise products (i.e., he multiplied each of the written numbers with each other). Among them, there turned out to be exactly 15 negative products. How many zeros were written on the board?

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