
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  $ABCD$  be a square with the side of  $20$  units. Amir divides this square into  $400$  unit squares. Reza then picks  $4$  of the vertices of these unit squares. These vertices lie inside the square  $ABCD$  and define a rectangle with the sides parallel to the sides of the square  $ABCD.$  There are exactly  $24$  unit squares which have at least one point in common with the sides of this rectangle. Find all possible values for the area of a rectangle with these properties.

<details><summary>Note</summary>*Note:* Vid changed to Amir, and Eva change to Reza!</details>

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