
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 an arrangement of the tables in rows and columns 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. If there must be at least two tables in every row and column and all of the tables in the room must be included, how many arrays are possible in a room containing $49$ tables? Note that $7$ rows of $7$ tables is different from $49$ rows of $1$ table (which is not allowed).

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