
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 different balls are to be placed into five boxes numbered 1, 2, 3, 4, and 5. (Write the result as a number)  
(1) How many ways can there be with at least one ball in box number 1?  
(2) How many ways are there to have exactly two empty boxes?  
(3) How many ways are there to have exactly three empty boxes?  
(4) How many ways are there such that the box number containing ball A is not less than the box number containing ball B?

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