
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
In a school with 1000 students, numbered from 1 to 1000, a group of 500 students is called a 'good group' if there exists a student in the group whose number divides the number of another student in the group. Otherwise, the group is called a 'bad group'. For example, the 500 students with numbers 1 to 500 form a 'good group' because student number 13 divides student number 26, and both are in the group. A 'good student' is defined as a student who does not belong to any 'bad group'. Find the student with the largest number among the 'good students'.

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