
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 boys and 4 girls standing in a row. How many arrangements are there that satisfy the following conditions? (Express your answers in mathematical notation)
(I) The 4 girls are standing together;
(II) No two girls are standing adjacent to each other;
(III) The boys, labeled A, B, and C, are standing in alphabetical order.

There are 6 different books to be distributed according to the following rules. How many distribution methods are there in each case?
(I) A gets 1 book, B gets 2 books, and C gets 3 books;
(II) The books are divided evenly into 3 piles;
(III) A, B, and C each get at least 1 book.

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