
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 4 newly graduated teachers to be assigned to four schools, with each teacher having a different assignment (represented by numbers).
1. How many different assignment schemes are there in total?
2. How many different assignment schemes are there if exactly one school is not assigned any teachers?
3. How many different assignment schemes are there if a certain school is assigned 2 teachers?
4. How many different assignment schemes are there if exactly two schools are not assigned any teachers?

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