
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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At a school, 30 students are enrolled in at least one of two clubs: Art or Music. 22 students are in the Art club and 25 students are in the Music club. If two students are selected at random from the list of enrolled students, what is the probability that the selected students can provide information about both clubs? Express your answer as a fraction in simplest form.

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