
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
To promote mathematical culture and stimulate students' interest in learning, a certain school launched a mathematics subject month activity. The seventh grade conducted four projects: $A$. Reading mathematical classics; $B$. Telling mathematical stories; $C$. Making mathematical models; $D$. Challenging mathematical games. Seventh graders are required to participate in only one project per person. Two students, Fanfan and Lelle, are interested in all four projects and do not know how to choose. So, the two of them decided to use a drawing method to choose. The two students stipulated: there are four small balls in an opaque bag labeled with the letters $A$, $B$, $C$, $D$, representing the four projects, with all other aspects of these small balls being the same, stirred and placed in the bag. Fanfan first draws one out of the bag at random and chooses the project represented by the letter on that small ball; Lelle then draws one out of the remaining three balls in the bag at random and chooses the project represented by the letter on that small ball.<br/>$(1)$ "Fanfan draws a ball labeled with the letter $D$" belongs to the ______ event; (Fill in "certain," "random," or "impossible")<br/>$(2)$ Please use a list or draw a tree diagram to find the probability that neither of them selected the project "$D$. Challenging mathematical games."

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