
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 colored every other column gray, starting with the very left column, and then he colored every other row gray, starting with the very top row. All cells adjacent to the boundary of the rectangle ended up being colored.

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

An example of coloring a \(5 \times 7\) rectangle is shown below:

![](https://cdn.mathpix.com/cropped/2024_05_06_5b323dccc142e96a9907g-32.jpg?height=226&width=311&top_left_y=448&top_left_x=575)

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