
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 through 4, into three boxes labeled A, B, and C.
(1) If none of the boxes are empty and ball number 3 must be placed in box B, how many different arrangements are there?
(2) If ball number 1 cannot be placed in box A and ball number 2 cannot be placed in box B, how many different arrangements are there? (Please formulate your answer before providing the numerical solution).

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