
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
A three-digit number with no zeros is written on the board. Petya wrote down in his notebook all the different numbers that can be obtained from the original number by permuting the digits (including the number written on the board). The sum of all the numbers Petya wrote down in his notebook turned out to be 444. What could the original number on the board have been?

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