
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 positive integer  $n$ , let  $f(n)$  be the greatest common divisor of all numbers obtained by permuting the digits of  $n$ , including the permutations that have leading zeroes. For example,  $f(1110)=\gcd(1110,1101,1011,0111)=3$ . Among all positive integers  $n$  with  $f(n) \neq n$ , what is the largest possible value of  $f(n)$ ?

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