
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
On the sides of the right triangle, outside are constructed regular nonagons, which are constructed on one of the catheti and on the hypotenuse, with areas equal to  $1602$    $cm^2$  and  $2019$    $cm^2$ , respectively. What is the area of the nonagon that is constructed on the other cathetus of this triangle?

(Vladislav Kirilyuk)

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