
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
How many different ways can 6 different books be distributed according to the following requirements?  
(1) Among three people, A, B, and C, one person gets 1 book, another gets 2 books, and the last one gets 3 books;  
(2) The books are evenly distributed to A, B, and C, with each person getting 2 books;  
(3) The books are divided into three parts, with one part getting 4 books and the other two parts getting 1 book each;  
(4) A gets 1 book, B gets 1 book, and C gets 4 books.

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