
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
Karolína drew a square with a side of $6 \mathrm{~cm}$. On each side of the square, she marked two points in blue, dividing the respective side into three equal parts. Then she constructed a quadrilateral that had all vertices blue and no two vertices lay on the same side of the square.

What are the possible areas of the quadrilaterals Karolína could have obtained? List all possibilities.

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