
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, we need to put all the balls into the boxes.  
(1) How many ways are there to do this?  
(2) How many ways are there to do this such that exactly one box remains empty?

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