
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 \(X\) be the set of positive integers that contain distinct digits in their decimal representation. If \(n \in X\), let \(A_{n}\) denote the set of numbers that can be formed by permuting the digits of \(n\), and let \(d_{n}\) denote the greatest common divisor of the elements of \(A_{n}\). What is the maximum value of \(d_{n}\)?

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