
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
Four students with the numbers $1$, $2$, $3$, $4$ respectively, are seated on seats numbered $1$, $2$, $3$, $4$ respectively.<br/>$(1)$ Each seat is occupied by exactly one student. Find the number of ways in which exactly two students have matching seat and student numbers.<br/>$(2)$ Each seat is occupied by exactly one student. Find the number of ways in which no student has matching seat and student numbers.<br/>$(3)$ Each seat is occupied by exactly one student. Find the number of ways in which the students with numbers $1$ and $2$ must sit together.

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