
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
Let  $K$  and  $L$  be positive integers. On a board consisting of  $2K \times 2L$  unit squares an ant starts in the lower left corner square and walks to the upper right corner square. In each step it goes horizontally or vertically to a neighbouring square. It never visits a square twice. At the end some squares may remain unvisited.
In some cases the collection of all unvisited squares forms a single rectangle. In such cases, we call this rectangle *MEMOrable*.

Determine the number of different MEMOrable rectangles.

*Remark: Rectangles are different unless they consist of exactly the same squares.*

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