
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
Given the rectangular cake, determine the maximum possible number of pieces the chef can create when cutting the cake with straight cuts parallel to the sides to obtain an equal number of pieces in the two central rows to the number of pieces on the perimeter of the cake.

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