
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
Distribute 4 newly transferred students into 4 designated classes in the 10th grade, with no limit on the number of students per class.

(1) Calculate the probability that each class receives 1 new student;

(2) Calculate the probability that at least one class does not receive any new students;

(3) Calculate the probability that exactly one class does not receive any new students.

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