
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
Let's call a four-digit number \(x\) amusing if each of its digits can be increased or decreased by 1 (where the digit 9 can only be decreased and the digit 0 can only be increased) so that the resulting number is divisible by \(x\).

a) Find two amusing numbers.
b) Find three amusing numbers.
c) Are there four amusing numbers?

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