
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
A school has eight identical copies of a specific textbook. Every day, some number of these textbooks are available in the classroom and some are taken by students for homework. Find the number of ways in which this distribution can occur if at least two books must be available in the classroom and at least three books must be taken by students.

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