
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 $(abc)$ and to form the numbers $(acb)$, $(bca)$, $(bac)$, $(cab)$, and $(cba)$. The participant adds these five numbers and reveals their sum as $N$. If given $N$, the magician can deduce the original number $(abc)$. Assume now that the total sum reported is $N=3306$. Determine the original three-digit number $(abc)$.

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