
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 rectangular array of books is an arrangement of the books in rows and columns such that each row contains the same number of books as every other row and each column contains the same number of books as every other column. If there must be at least three books in every row and column and all of the books in the room must be included, how many arrays are possible in a library room containing $48$ books? Note that $16$ rows of $3$ books is different from $3$ rows of $16$ books.

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