
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 the numbers \(1, 2, 3, \ldots, 1000\). Find the largest number \(m\) with the following property: no matter which \(m\) of these numbers are removed, among the remaining \(1000-m\) numbers, there will be two such that one of them divides the other.

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