
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 \(a\), \(S(a)\) represents the sum of the digits of \(a\) (for example, \(S(123) = 1 + 2 + 3 = 6\)). If the digits of a natural number \(n\) are all different and \(S(3n) = 3S(n)\), what is the maximum value of \(n\)?

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