
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
At a killers' convention, 1000 participants attended, each receiving a registration number from 1 to 1000. By the end of the convention, it turned out that all the killers except for number 1 were dead. It is known that each killer could only kill killers with larger numbers, and the number of their victims could not exceed their own number. What is the minimum number of killers who could have participated in the killings at the convention?

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