
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 dining table arrangement requires placing $48$ identical plates such that each row and each column contains the same number of plates, and each row and column has at least two plates. Determine how many different arrangements (configurations of rows and columns) are possible if we assume all plates are used and the arrangement respects the condition mentioned. Note that configurations are considered distinct based on the orientation (i.e., swapping rows and columns counts as different).

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