
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
In a similar parlor game, the magician asks a participant to think of a three-digit number $(abc)$. The participant then forms the numbers $(acb)$, $(bca)$, $(bac)$, $(cab)$, and $(cba)$, adds these five numbers, and reveals their sum, $N$, to the magician. If given $N = 4422$, determine the original number $(abc)$, knowing that the sum of the digits $(a+b+c)$ must be at least 18.

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