
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, all the balls need to be placed into the boxes.  
(1) How many methods are there without any empty boxes?  
(2) How many methods are there allowing empty boxes?  
(3) How many methods are there exactly with one box left empty? (Answer with a number)

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