
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 has probabilities of being solved independently by person \( A \), \( B \), and \( C \) as \( \frac{1}{a} \), \( \frac{1}{b} \), and \( \frac{1}{c} \) respectively, where \( a \), \( b \), and \( c \) are positive integers less than 10. When \( A \), \( B \), and \( C \) work on the problem simultaneously and independently, the probability that exactly one of them solves the problem is \( \frac{7}{15} \). Determine the probability that none of the three persons solve the problem.

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