
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
A three-digit number has digits _\\(a\\)_, _\\(b\\)_, and _\\(c\\)_ in the hundreds, tens, and units places, respectively. A three-digit number is considered a "fateful number" if and only if the sum of any two digits equals the third digit (such as \\(213\\), \\(134\\), etc.). If _\\(a\\)_, _\\(b\\)_, and _\\(c\\)_ belong to \\(\\{1,2,3,4\\}\\) and are distinct from each other, then the probability that this three-digit number is a "fateful number" is          .

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