
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 high school class, five students from Grade 11, Class 1, signed up for extracurricular activities. There are three projects available: "Online Journalists," "Robot Action," and "Sounds of Music." Each student must sign up for one project only.  
$(1)$ Find the number of ways in which "each project has at least one student signed up."  
$(2)$ Given that exactly three students signed up for one project, find the probability that only student A signed up for the "Online Journalists" project.

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