
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
To bring luck to Libor, a natural number must have its square divisible by 7, 8, 9, and 10. Find all natural numbers less than 1000 that bring luck to Libor.

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