
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 game, the magician asks a participant to think of a three-digit number \( (abc) \) and then to create the numbers \( (acb), (bac), (bca), (cab), (cba) \). The participant is asked to add these numbers and tell the sum, \( S \). If the magician is told \( S = 4239 \), determine the original number \( (abc) \).

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