
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
Given the probabilities of three events, \( A_{1}, A_{2}, A_{3} \), which form a complete set: \( p_{1} = P\left(A_{1}\right) = 0.22 \), \( p_{2} = P\left(A_{2}\right) = 0.31 \), \( p_{3} = P\left(A_{3}\right) = 0.47 \). Conduct five trials, each of which results in one of the three events.

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