
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
(The full score of this question is 12 points) There are 4 different balls and 4 different boxes. Now, all the balls need to be placed into the boxes.  
(1) If exactly one box is left empty, how many methods are there?  
(2) If exactly two boxes are left empty, how many methods are there?

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