
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  $N$  be a 3-digit number with three distinct non-zero digits. We say that  $N$  is *mediocre* if it has the property that when all six 3-digit permutations of  $N$  are written down, the average is  $N$ . For example,  $N = 481$  is mediocre, since it is the average of  $\{418, 481, 148, 184, 814, 841\}$ .

Determine the largest mediocre number.

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