
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 where the two legs are equal, a square is inscribed such that its side serves as one-half of the leg of the triangle. If this square has an area of $289\, \text{cm}^2$, find the area of a second square, also inscribed in the same triangle, where the side of this square aligns with the hypotenuse and reaches to the midpoint of the hypotenuse.

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