
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
Place four balls numbered 1, 2, 3, and 4 into three boxes labeled A, B, and C.  
(1) If no box is empty and ball number 3 must be in box B, how many different arrangements are there?  
(2) If ball number 1 is not in box A and ball number 2 is not in box B, how many different arrangements are there?

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