
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]


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There is a difficult math problem. In half an hour, the probabilities that person A and person B can solve it are both $\frac{1}{2}$, and the probability that person C can solve it is $\frac{1}{3}$. If the three individuals independently attempt to solve the problem within half an hour, the probability that the problem will be solved is ______.

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