
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
There are five students named A, B, C, D, and E. Find:<br/>$(1)$ In how many different ways can the five students stand in a row?<br/>$(2)$ In how many different ways can the five students stand in a row if A and B must be adjacent, and C and D cannot be adjacent?<br/>$(3)$ In how many different ways can the five students be assigned to three classes, with at least one student in each class?

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