
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
A certain brand of computers has a warranty period of $1$ year. Based on a large amount of repair record data, the maximum number of repairs for this brand of computers within one year is $3$ times, with $15\%$ needing $1$ repair, $6\%$ needing $2$ repairs, and $4\%$ needing $3$ repairs. <br/>$(1)$ If a person buys $1$ of this brand of computer, find the probabilities of the following events: $A=$"needs repair within the warranty period"; $B=$"does not need more than $1$ repair within the warranty period"; <br/>$(2)$ If a person buys $2$ of this brand of computers, and the need for repair within the warranty period for the $2$ computers is independent, find the probability that the total number of repairs for these $2$ computers within the warranty period does not exceed $2$ times.

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