
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 an isosceles right triangle, inscribe another isosceles right triangle in such a way that the vertices of the inscribed triangle lie on the interior points of the sides of the given triangle. Which of the inscribed triangles has the smallest area, and what fraction of the area of the given triangle does this smallest area represent?

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