
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
In a recruitment exam, there are three different type-A questions numbered $1$, $2$, $3$, and two different type-B questions numbered $4$, $5$.

    $(1)$ If person A randomly selects one question from each of the type-A and type-B categories, and we use the symbol $(x,y)$ to represent the event "the numbers of the questions drawn from type-A and type-B categories are $x$ and $y$ respectively, and $x < y$", then how many basic events are there? Please list them.

    $(2)$ If person A randomly selects two questions from the five questions, what is the probability that the sum of their numbers is less than $8$ but not less than $4$?

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