
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
Consider a rectangular tiled room with dimensions  $m\times n$ , where the tiles are  $1\times1$  in size. Compute all ordered pairs  $(m,n)$  with  $m\leq n$  such that the number of tiles on the perimeter is equal to the number of tiles in the interior (i.e. not on the perimeter).

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