
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
Four balls are placed into four boxes labeled 1, 2, 3, and 4. Determine the number of different ways to place the balls according to the following conditions:
(1) The four balls are distinct, and exactly one box is left empty;
(2) The four balls are identical, and exactly one box is left empty;
(3) The four balls are distinct, and empty boxes are allowed;
(4) The four balls are identical, and empty boxes are allowed.

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