
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
Given a finite set of cards. Each card has either the number 1 or the number -1 written on it (each card has exactly one number). There are 100 more cards with -1 than cards with 1. If you find the product of the numbers on each pair of different cards and sum all these products, the result is 1000. How many cards have the number 1?

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