
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. All the balls need to be placed into the boxes.
(1) If exactly one box remains empty, how many different arrangements are possible?
(2) If exactly two boxes remain empty, how many different arrangements are possible?

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