
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 tables is arranged such that each row contains the same number of tables as every other row, and each column contains the same number of tables as every other column. With at least two tables in every row and column, how many such arrays are possible in a meting room containing $48$ tables? Note that $12$ rows of $4$ tables is considered different from $4$ rows of $12$ tables.

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