
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 implement the "double reduction" policy and promote intangible cultural heritage, a certain school plans to organize extracurricular interest classes for students to visit the following projects: $A$ (Xiu Shui pottery art), $B$ (Xiu Shui tea-picking opera), $C$ (Jiujiang mountain song), $D$ (Dean Pan opera). Xiao Ming and Xiao Han randomly sign up to visit one of them.  
$(1)$ The event "Xiao Ming visits Jiujiang mountain song" is ________; (Please fill in the number of the correct answer on the line)  
① a certain event;  
② an impossible event;  
③ a random event.  
$(2)$ Please calculate the probability that both Xiao Ming and Xiao Han will visit intangible cultural heritage projects in Xiu Shui using a list or tree diagram method.

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