
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 5 different balls and 5 different boxes. Now, we want to put all the balls into the boxes.  
(1) How many ways are there to do this?  
(2) If exactly one box is left empty, how many ways are there to do this?  
(3) If exactly two boxes are left empty, how many ways are there to do this?

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