
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
As the saying goes, "Three cobblers with their wits combined equal Zhuge Liang in wisdom." In a provincial math team competition, three students from a certain school each solved a problem with probabilities of $\frac{1}{5}$, $\frac{1}{3}$, and $\frac{1}{4}$, respectively. Given their team spirit, the probability that the problem is solved is \_\_\_\_\_\_.

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