
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
For a natural number \( N \), if at least five of the natural numbers from 1 to 9 can divide \( N \), then \( N \) is called a "five-rule number." What is the smallest "five-rule number" greater than 2000?

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