
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 one type of book and four identical copies of a second type of book. At any given time, some of these books are at the library and some are checked out. 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 of each type is in the library and at least one of each type is checked out?

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