
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 9 different extracurricular books to be distributed among three students, A, B, and C. Determine the number of ways the books can be distributed under the following conditions:
(1) A gets 4 books, B gets 3 books, and C gets 2 books;
(2) One student gets 4 books, another gets 3 books, and the last gets 2 books;
(3) A, B, and C each get 3 books.

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