
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

In a right isosceles triangle \( ABC \) with a right angle at vertex \( B \), a rectangle \( MNKB \) is inscribed such that two vertices \( M \) and \( B \) lie on the legs and vertex \( N \) lies on the hypotenuse \( AC \). In what ratio must point \( N \) divide the hypotenuse so that the area of the rectangle is 18% of the area of the triangle?

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