
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, and all the balls need to be placed into the boxes.  
(1) If exactly one box is left empty, find the number of different ways to place the balls;  
(2) If exactly two boxes are left empty, find the number of different ways to place the balls.

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