
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
There are 6 different books to be distributed by the following methods, how many ways can each be done:  
(1) Distributed to three people, A, B, and C, each getting 2 books;  
(2) Distributed to three people, A, B, and C, with A getting 1 book, B getting 2 books, and C getting 3 books;  
(3) Distributed to three people, A, B, and C, with one person getting 1 book, another getting 2 books, and the last one getting 3 books.

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