
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 library has eight identical copies of a particular book. Some of these books can be either at the library or checked out at any given time. How many different ways are there for some of the books to be in the library and the rest to be checked out if at least one book must be in the library and at least one must be checked out?

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