
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 math competition problem: The probabilities that A, B, and C solve the problem independently are $\frac{1}{a}$, $\frac{1}{b}$, and $\frac{1}{c}$ respectively, where $a$, $b$, and $c$ are all single-digit numbers. If A, B, and C attempt the problem independently and the probability that exactly one of them solves the problem is $\frac{7}{15}$, then the probability that none of them solves the problem is $\qquad$.

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