
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
If \( n \) is a positive integer, we denote by \( n! \) the product of all integers from 1 to \( n \). For example, \( 5! = 1 \times 2 \times 3 \times 4 \times 5 = 120 \) and \( 13! = 1 \times 2 \times 3 \times 4 \times 5 \times \cdots \times 12 \times 13 \). By convention, we write \( 0! = 1! = 1 \). Find three distinct integers \( a \), \( b \), and \( c \) between 0 and 9 such that the three-digit number \( abc \) is equal to \( a! + b! + c! \).

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