
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
Leonid has a white checkered rectangle. First, he painted in gray all columns through one, starting from the leftmost one, and then all rows through one, starting from the topmost one. All cells adjacent to the border of the rectangle turned out to be painted.

How many painted cells could there be in the rectangle if there are 74 white cells left? List all possible options.

An example of a painted rectangle $5 \times 7$ is shown below.

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