
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
$n$ numbers are written on a board, satisfying the following properties:

- All numbers have 3 digits
- None contain a 0
- Two different numbers never have the same digit in the hundreds place, the same digit in the tens place, or the same digit in the units place
- The sum of the digits of each number is 9

What is the maximum possible value for $n$?

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