
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, the "magician" asks a person to randomly think of a three-digit number ($abc$), where $a, b, c$ are the digits of this number. They then ask this person to arrange the digits into 5 different numbers: $(acb)$, $(bac)$, $(bca)$, $(cab)$, and $(cba)$. The magician then asks for the sum of these 5 numbers, denoted as $N$. Once the magician knows $N$, they can determine the original number ($abc$).

Given that $N=3194$, assume the role of the "magician" and determine the original number ($abc$).

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