
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 triangle ABC, angle BAC is a right angle, and AB = AC. Each side of the triangle has a square constructed on it, with the square on side BC being the largest. The sum of the areas of the three squares is 450 square centimeters. Determine the area of the square constructed on side BC.

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