
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 four boxes numbered 1, 2, 3, and 4, and four balls. The task is to place all the balls into the boxes. The questions are:  
(1) How many different ways are there to do this?  
(2) How many ways are there to do this if exactly one box is left empty?  
(3) How many ways are there to do this if exactly two boxes are left empty?

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