
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
There is a difficult math problem. The probability that person A can solve it within half an hour is \( \dfrac{1}{2} \), and the probability that person B can solve it is \( \dfrac{1}{3} \). If both try to solve it independently within half an hour, the probability that neither of them solves it is \_\_\_\_\_\_\_\_, and the probability that the problem is solved is \_\_\_\_\_\_\_\_.

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