
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 certain game, a "magician" asks a person to think of a three-digit number \(\overline{abc}\) (where \(a, b, c\) are the digits in decimal form), and then asks this person to select 5 numbers: \(\overline{acb}\), \(\overline{bac}\), \(\overline{bca}\), \(\overline{cab}\), and \(\overline{cba}\). The sum of these 5 numbers is \(N\). The person tells \(N\) to the "magician", who can then correctly identify the original number \(\overline{abc}\). Given \(N = 3194\), act as the "magician" and determine the original number \(\overline{abc}\).

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