
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]


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In order to add cultural elements to the World Expo, the municipal government organized the activity of "intangible cultural heritage" entering the scenic area. Among them, the four intangible cultural heritage projects of "$A$, Jinzhou Gold Painting", "$B$, Yuhua Stone Color Painting", "$C$, Velvet Crochet Technique", and "$D$, Green Willow Spring Tea Art Making Technique" have all settled in the market of the scenic area. Xiao Ming and Xiao Gang, two classmates, plan to participate in social practice activities over the weekend and choose one of the four projects for an interview to understand the development process and cultural value of the project. 

$(1)$ The probability of Xiao Ming choosing the "Yuhua Stone Color Painting" project is ______;  
$(2)$ Using a tree diagram or list method, find the probability that Xiao Ming and Xiao Gang choose the same project for the interview.

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