
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 a right triangle with legs \(a\) and \(b\), squares are constructed, lying outside the triangle. Find the area of the triangle with vertices at the centers of the squares.

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