
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 different balls and 4 different boxes. Now we need to put all the balls into the boxes.  
(1) How many ways are there to do this? (Answer with a number)  
(2) If exactly one box is left empty, how many ways are there to do this? (Answer with a number)  
(3) If exactly two boxes are left empty, how many ways are there to do this? (Answer with a number)

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