
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 distinct balls and 4 distinct boxes. Place all the balls into the boxes.
(1) If exactly one box remains empty, how many ways are there to do this?
(2) If exactly one box contains two balls, how many ways are there to select this?
(3) If exactly two boxes remain empty, how many ways are there to do this?

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