
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
Find all three-digit numbers \(A\) that have the property that the arithmetic mean of all numbers obtained by rearranging the digits of \(A\) is still equal to \(A\).

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